775:
296:
794:(1+10 pages) (NB. This work was partially presented at CDS-92 Conference, Kaliningrad, Russia, on 1992-09-07 and at the IEEE Symposium on Information Theory, San Antonio, TX, USA.)
140:
90:
488:
388:
354:
655:
Greferath, Marcus (2009). "An
Introduction to Ring-Linear Coding Theory". In Sala, Massimiliano; Mora, Teo; Perret, Ludovic; Sakata, Shojiro; Traverso, Carlo (eds.).
446:
426:
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175:
1125:
1164:
1090:
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895:
712:
676:
664:
1085:
1311:
1179:
1120:
992:
637:
1027:
1207:
452:(which is circular since the group is cyclic) between them. More generally, the Lee distance between two strings of length
848:
1212:
1067:
323:
this is not the case anymore; the Lee distance between single letters can become bigger than 1. However, there exists a
1291:
1017:
505:
1141:
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832:
790:
1306:
1202:
1146:
1001:
40:
1105:
1301:
1037:
1347:
1250:
818:
95:
45:
1342:
911:
822:
459:
359:
1255:
1197:
1057:
985:
316:, because both distances are 0 for two single equal symbols and 1 for two single non-equal symbols. For
598:
330:
1062:
169:
827:
586:
1260:
887:
704:
594:
1189:
1156:
767:
751:
501:
398:
817:(in English and German). Oberpfaffenhofen, Germany: Institute of Communications and Navigation,
668:
1321:
957:
891:
759:
708:
692:
672:
633:
542:
948:
Voloch, Jose Felipe; Walker, Judy L. (1998). "Lee
Weights of Codes from Elliptic Curves". In
1316:
1286:
1240:
1042:
978:
925:
875:
743:
696:
656:
313:
1169:
1110:
1022:
949:
936:
876:
697:
1222:
1115:
590:
431:
411:
391:
1336:
1032:
1009:
854:
771:
729:
657:
324:
28:
1235:
538:
491:
449:
1245:
625:
17:
804:
Strang, Thomas; Dammann, Armin; Röckl, Matthias; Plass, Simon (October 2009).
621:
579:
929:
763:
755:
589:
is an example of code in the Lee metric. Other significant examples are the
792:
151:
36:
1281:
805:
456:
is the length of the shortest path between them in the Cayley graph of
747:
699:
Algebraic Codes on Lines, Planes, and Curves: An
Engineering Approach
582:
while the
Hamming distance is used in case of orthogonal modulation.
291:{\displaystyle \sum _{i=1}^{n}\min(|x_{i}-y_{i}|,\,q-|x_{i}-y_{i}|).}
597:; these codes are non-linear when considered over a field, but are
1265:
815:
6. GI/ITG KuVS FachgesprÀch
Ortsbezogene Anwendungen und Dienste
974:
954:
Codes, Curves, and
Signals: Common Threads in Communications
970:
541:
induced by the Lee distance is a discrete analog of the
572:
The Lee distance is named after
William Chi Yuan Lee (
462:
434:
414:
362:
333:
178:
98:
48:
1274:
1221:
1188:
1155:
1134:
1076:
1008:
516:. The analogous quotient metric on a quotient of
482:
440:
420:
382:
348:
290:
134:
84:
910:Lee, C. Y. (1958), "Some properties of nonbinary
560:, then the Lee distance between 3140 and 2543 is
200:
650:
648:
397:Considering the alphabet as the additive group
408:, the Lee distance between two single letters
986:
573:
8:
853:Thomas Strang; et al. (October 2009).
993:
979:
971:
855:"Using Gray codes as Location Identifiers"
522:modulo an arbitrary lattice is known as a
956:. Springer Science & Business Media.
826:
474:
469:
464:
461:
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413:
374:
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215:
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177:
126:
113:
103:
97:
76:
63:
53:
47:
1165:Comparison of regular-expression engines
807:Using Gray codes as Location Identifiers
735:IEEE Transactions on Information Theory
659:Gröbner Bases, Coding, and Cryptography
610:
917:IRE Transactions on Information Theory
703:. Cambridge University Press. p.
632:(3rd ed.), Elsevier, p. 52,
616:
614:
490:. This can also be thought of as the
448:is the length of shortest path in the
327:(weight-preserving bijection) between
1126:ZhuâTakaoka string matching algorithm
665:Springer Science & Business Media
135:{\displaystyle y_{1}y_{2}\dots y_{n}}
85:{\displaystyle x_{1}x_{2}\dots x_{n}}
7:
483:{\displaystyle \mathbf {Z} _{q}^{n}}
383:{\displaystyle \mathbb {Z} _{2}^{2}}
312:the Lee distance coincides with the
1091:BoyerâMoore string-search algorithm
25:
1180:Nondeterministic finite automaton
1121:Two-way string-matching algorithm
465:
349:{\displaystyle \mathbb {Z} _{4}}
838:from the original on 2015-05-01
781:from the original on 2020-12-17
1096:BoyerâMooreâHorspool algorithm
1086:ApostolicoâGiancarlo algorithm
730:"Codes over Gaussian Integers"
728:Huber, Klaus (January 1994) .
282:
278:
250:
235:
207:
203:
1:
878:Introduction to Coding Theory
1101:KnuthâMorrisâPratt algorithm
1028:DamerauâLevenshtein distance
574:
1292:Compressed pattern matching
1018:Approximate string matching
578:). It is applied for phase
1364:
1297:Longest common subsequence
1208:NeedlemanâWunsch algorithm
1078:String-searching algorithm
884:Cambridge University Press
1307:Sequential pattern mining
1147:Commentz-Walter algorithm
1135:Multiple string searching
1068:WagnerâFischer algorithm
1317:String rewriting systems
1302:Longest common substring
1213:SmithâWaterman algorithm
1038:Gestalt pattern matching
930:10.1109/TIT.1958.1057446
494:resulting from reducing
356:with the Lee weight and
1251:Generalized suffix tree
1175:Thompson's construction
941:Algebraic Coding Theory
819:German Aerospace Center
774:. IEEE Log ID 9215213.
630:Dictionary of Distances
568:History and application
1203:Hirschberg's algorithm
912:error-correcting codes
484:
442:
422:
384:
350:
292:
199:
136:
86:
1058:Levenshtein automaton
1048:JaroâWinkler distance
485:
443:
423:
385:
351:
293:
179:
137:
87:
1106:RabinâKarp algorithm
1063:Levenshtein distance
460:
432:
412:
360:
331:
176:
96:
46:
1261:Ternary search tree
937:Berlekamp, Elwyn R.
479:
379:
1190:Sequence alignment
1157:Regular expression
874:Roth, Ron (2006).
693:Blahut, Richard E.
599:linear over a ring
502:Manhattan distance
480:
463:
438:
418:
380:
363:
346:
288:
132:
82:
1330:
1329:
1322:String operations
963:978-1-4615-5121-8
897:978-0-521-84504-5
748:10.1109/18.272484
714:978-1-139-46946-3
678:978-3-540-93806-4
562:1 + 2 + 0 + 3 = 6
532:Mannheim distance
441:{\displaystyle y}
421:{\displaystyle x}
16:(Redirected from
1355:
1287:Pattern matching
1241:Suffix automaton
1043:Hamming distance
995:
988:
981:
972:
967:
950:Vardy, Alexander
944:
932:
902:
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339:
322:
314:Hamming distance
311:
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297:
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276:
275:
263:
262:
253:
238:
233:
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220:
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142:of equal length
141:
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1331:
1326:
1270:
1217:
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1170:Regular grammar
1151:
1130:
1111:Raita algorithm
1072:
1023:Bitap algorithm
1004:
999:
964:
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935:
909:
906:
905:
898:
873:
872:
868:
852:
841:
839:
835:
828:10.1.1.398.9164
810:
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798:
784:
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778:
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726:
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686:
679:
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640:
620:
619:
612:
607:
570:
561:
554:
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526:Mannheim metric
525:
524:
517:
508:
495:
492:quotient metric
458:
457:
453:
430:
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358:
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329:
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267:
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162:
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122:
109:
99:
94:
93:
72:
59:
49:
44:
43:
23:
22:
18:Mannheim metric
15:
12:
11:
5:
1361:
1359:
1351:
1350:
1348:String metrics
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1223:Data structure
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1123:
1118:
1116:Trigram search
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863:
796:
742:(1): 207â216.
720:
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684:
677:
644:
638:
609:
608:
606:
603:
591:Preparata code
587:Berlekamp code
569:
566:
550:
547:
543:elliptic space
477:
472:
467:
437:
417:
402:
392:Hamming weight
377:
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287:
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79:
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52:
24:
14:
13:
10:
9:
6:
4:
3:
2:
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1346:
1344:
1343:Coding theory
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1059:
1056:
1054:
1051:
1049:
1046:
1044:
1041:
1039:
1036:
1034:
1033:Edit distance
1031:
1029:
1026:
1024:
1021:
1019:
1016:
1015:
1013:
1011:
1010:String metric
1007:
1003:
996:
991:
989:
984:
982:
977:
976:
973:
965:
959:
955:
951:
946:
943:, McGraw-Hill
942:
938:
934:
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834:
829:
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769:
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749:
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724:
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694:
688:
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639:9783662443422
635:
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588:
583:
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493:
475:
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451:
435:
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407:
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401:
395:
393:
375:
370:
341:
326:
325:Gray isometry
320:
315:
309:
302:
285:
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268:
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259:
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246:
243:
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119:
114:
110:
104:
100:
77:
73:
69:
64:
60:
54:
50:
42:
38:
34:
30:
29:coding theory
19:
1236:Suffix array
1142:AhoâCorasick
1053:Lee distance
1052:
953:
940:
924:(2): 77â82,
921:
915:
877:
869:
859:ResearchGate
858:
847:(5/8 pages)
840:. Retrieved
814:
806:
799:
783:. Retrieved
739:
733:
723:
698:
687:
658:
629:
626:Deza, Michel
595:Kerdock code
584:
571:
555:
552:
539:metric space
536:
531:
523:
518:
512:
509:
496:
450:Cayley graph
403:
399:
396:
318:
307:
300:
163:
156:
147:
143:
39:between two
33:Lee distance
32:
26:
1246:Suffix tree
861:(Abstract).
622:Deza, Elena
504:modulo the
172:defined as
168:. It is a
1337:Categories
886:. p.
842:2020-12-16
785:2020-12-17
667:. p.
605:References
580:modulation
161:} of size
155:{0, 1, âŠ,
823:CiteSeerX
772:195866926
764:0018-9448
756:1557-9654
500:with the
390:with the
265:−
247:−
222:−
181:∑
159:− 1
146:over the
120:…
70:…
939:(1968),
833:Archived
776:Archived
695:(2008).
628:(2014),
152:alphabet
37:distance
1312:Sorting
1282:Parsing
1002:Strings
952:(ed.).
821:(DLR).
549:Example
506:lattice
41:strings
960:
894:
825:
770:
762:
754:
711:
675:
636:
321:> 3
170:metric
31:, the
1275:Other
1231:DAFSA
1198:BLAST
836:(PDF)
811:(PDF)
779:(PDF)
768:S2CID
752:eISSN
150:-ary
35:is a
1266:Trie
1256:Rope
958:ISBN
892:ISBN
760:ISSN
709:ISBN
673:ISBN
634:ISBN
593:and
585:The
537:The
428:and
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888:314
744:doi
705:108
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575:æć§ć
558:= 6
553:If
530:or
310:= 3
305:or
303:= 2
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201:min
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890:.
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671:.
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647:^
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613:^
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497:Z
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436:y
416:x
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400:Z
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371:2
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319:q
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283:)
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