Hamming graphs and special LCD codes

被引：4

作者：

Fish, W. ^{[1
]}

Key, J. D. ^{[1
]}

Mwambene, E. ^{[1
]}

Rodrigues, B. G. ^{[2
]}

机构：

[1] Univ Western Cape, Dept Math & Appl Math, ZA-7535 Bellville, South Africa

[2] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, ZA-4000 Durban, South Africa

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2019年 / 61卷 / 1-2期

基金：

新加坡国家研究基金会; 芬兰科学院;

关键词：

LCD codes; Hamming graphs; Decoding; PERMUTATION DECODING SETS; BINARY-CODES; LINEAR CODES; COMPLEMENTARY DUALS; INCIDENCE MATRICES; TERNARY CODES;

D O I：

10.1007/s12190-019-01259-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Codes from adjacency matrices from the Hamming graphs Hk(n,m) are examined for the property of being special LCD codes. The special property involves being able to propose a feasible decoding algorithm for the binary codes, and also to deduce the dimension of the code from the eigenvalues of an adjacency matrix, which are known for these graphs. Some positive results are obtained, in particular for the binary and ternary codes.

引用

页码：461 / 479

页数：19

共 50 条

[41] On an isoperimetric problem for Hamming graphs
Harper, LH
[J]. DISCRETE APPLIED MATHEMATICS, 1999, 95 (1-3) : 285 - 309
[42] RADIO GRACEFUL HAMMING GRAPHS
Niedzialomski, Amanda
[J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2016, 36 (04) : 1007 - 1020
[43] Combinatorial PDEs on Hamming graphs
Barletta, E
Dragomir, S
[J]. DISCRETE MATHEMATICS, 2002, 254 (1-3) : 1 - 18
[44] Spectral characterization of the Hamming graphs
Bang, Sejeong
van Dam, Edwin R.
Koolen, Jack H.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (11-12) : 2678 - 2686
[45] Retracts of infinite Hamming graphs
Chastand, M
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1997, 71 (01) : 54 - 66
[46] ISOMETRIC EMBEDDINGS IN HAMMING GRAPHS
WILKEIT, E
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1990, 50 (02) : 179 - 197
[47] 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
[48] Characterizing subgraphs of Hamming graphs
Klavzar, S
Peterin, I
[J]. JOURNAL OF GRAPH THEORY, 2005, 49 (04) : 302 - 312
[49] Error correcting codes2. The Hamming codes
Priti Shankar
[J]. Resonance, 1997, 2 (1) : 34 - 43
[50] On LCD MRD Codes
Shi, Minjia
Huang, Daitao
[J]. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2018, E101A (09) : 1599 - 1602

← 1 2 3 4 5 →