COMPLETELY REGULAR CODES BY CONCATENATING HAMMING CODES

被引：4

作者：

Borges, Joaquim ^{[1
]}

Rifa, Josep ^{[1
]}

Zinoviev, Victor ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Informat & Commun Engn, Barcelona, Spain

[2] Russian Acad Sci, A A Kharkevich Inst Problems Informat Transmiss, Moscow, Russia

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2018年 / 12卷 / 02期

关键词：

Completely regular codes; completely transitive codes; concatenation; extended codes; intersection array; TRANSITIVE CODES; GRAPHS;

D O I：

10.3934/amc.2018021

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of these codes. As a result, we find some non-equivalent completely regular codes, over the same finite field, with the same parameters and intersection array. We also study when the extension of these codes gives completely regular codes. Some of these new codes are completely transitive.

引用

页码：337 / 349

页数：13

共 50 条

[41] Hamming codes are rate-efficient array codes
Vallés, EL
Casado, AIV
Blaum, M
Villasenor, J
Wesel, RD
[J]. GLOBECOM '05: IEEE Global Telecommunications Conference, Vols 1-6: DISCOVERY PAST AND FUTURE, 2005, : 1320 - 1324
[42] WOM-CODES CONSTRUCTED FROM HAMMING CODES
GODLEWSKI, P
[J]. DISCRETE MATHEMATICS, 1987, 65 (03) : 237 - 243
[43] Intersection of Hamming codes avoiding Hamming subcodes
J. Rifà
F. I. Solov’eva
M. Villanueva
[J]. Designs, Codes and Cryptography, 2012, 62 : 209 - 223
[44] Intersection of Hamming codes avoiding Hamming subcodes
Rifa, J.
Solov'eva, F. I.
Villanueva, M.
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2012, 62 (02) : 209 - 223
[45] SUPERIMPOSED CODES IN THE HAMMING SPACE
ERICSON, T
LEVENSHTEIN, VI
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1994, 40 (06) : 1882 - 1893
[46] Hamming Graphs and Permutation Codes
Barta, Janos
Montemanni, Roberto
[J]. 2017 FOURTH INTERNATIONAL CONFERENCE ON MATHEMATICS AND COMPUTERS IN SCIENCES AND IN INDUSTRY (MCSI), 2017, : 154 - 158
[47] ELUSIVE CODES IN HAMMING GRAPHS
Hawtin, Daniel R.
Gillespie, Neil I.
Praeger, Cheryl E.
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2013, 88 (02) : 286 - 296
[48] OPTIMAL MODIFIED HAMMING CODES
AZUMI, S
KASAMI, T
[J]. ELECTRONICS & COMMUNICATIONS IN JAPAN, 1975, 58 (06): : 9 - 15
[49] ON A CATEGORIAL ISOMORPHISM BETWEEN A CLASS OF COMPLETELY REGULAR CODES AND A CLASS OF DISTANCE REGULAR GRAPHS
RIFACOMA, J
[J]. LECTURE NOTES IN COMPUTER SCIENCE, 1991, 508 : 164 - 179
[50] GENERALIZED HAMMING WEIGHTS OF MELAS CODES AND DUAL MELAS CODES
VANDERGEER, G
VANDERVLUGT, M
[J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 1994, 7 (04) : 554 - 559

← 1 2 3 4 5 →