LCD codes from adjacency matrices of graphs

Key, J. D.; Rodrigues, Bernardo Gabriel

doi:10.1007/s00200-017-0339-6

Cited by 14 publications

(4 citation statements)

References 16 publications

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“…An example of a zero hull when C = RC ⊥ is from Tables 3 and 4, where C 1 = W ⊥ 1 for n ≡ 4 (mod p), but RC 1 = W 1 , and from Corollary 2, Hull(W 1 ) = Hull(W ⊥ 1 ) = {0}. See also [16] for further results on LCD codes from graphs.…”

Section: Resultsmentioning

confidence: 99%

Codes from Adjacency Matrices of Uniform Subset Graphs

Fish

Key

Mwambene

2017

Graphs and Combinatorics

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Studies of the p-ary codes from the adjacency matrices of uniform subset graphs Γ (n, k, r) and their reflexive associates have shown that a particular family of codes defined on the subsets are intimately related to the codes from these graphs. We describe these codes here and examine their relation to some particular classes of uniform subset graphs. In particular we include a complete analysis of the p-ary codes from Γ (n, 3, r) for p ≥ 5, thus extending earlier results for p = 2, 3.

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Section: Resultsmentioning

confidence: 99%

Codes from Adjacency Matrices of Uniform Subset Graphs

Fish

Key

Mwambene

2017

Graphs and Combinatorics

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“…These codes have an important role in cryptography. Lately, there has been much interest and a lot of work has been done regarding this topic (see, e.g., [3,13,15]). The codes labeled with * in Table 1 are LCD codes.…”

Section: Computational Resultsmentioning

confidence: 99%

LDPC codes constructed from cubic symmetric graphs

Crnković¹,

Rukavina²,

Šimac³

2020

Preprint

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Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The constructed codes are (3, 3)-regular and the vast majority of the corresponding Tanner graphs have girth greater than four. We analyse properties of the obtained codes and present bounds for the code parameters, the dimension and the minimum distance. Furthermore, we give an expression for the variance of the syndrome weight of the constructed codes. Information on the LDPC codes constructed from bipartite cubic symmetric graphs with less than 200 vertices is presented as well. Some of the constructed codes are optimal, and some have an additional property of being self-orthogonal or linear codes with complementary dual (LCD codes).

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“…From [15,16]: , E) be a graph with adjacency matrix A. Let p be any prime, C = C p (A), RC = C p (RA) (for the reflexive graph), where RA = A + I.…”

Section: Background Concepts and Terminologymentioning

confidence: 99%

Binary codes from $ m $-ary $ n $-cubes $ Q^m_n $

Key¹,

Rodrigues²

2021

AMC

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We examine the binary codes from adjacency matrices of the graph with vertices the nodes of the m-ary n-cube Q m n and with adjacency defined by the Lee metric. For n = 2 and m odd, we obtain the parameters of the code and its dual, and show the codes to be LCD. We also find s-PD-sets of size s + 1 for s < m−1 2 for the dual codes, i.e. [m 2 , 2m − 1, m] 2 codes, when n = 2 and m ≥ 5 is odd.

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LCD codes from adjacency matrices of graphs

Cited by 14 publications

References 16 publications

Codes from Adjacency Matrices of Uniform Subset Graphs

Codes from Adjacency Matrices of Uniform Subset Graphs

LDPC codes constructed from cubic symmetric graphs

Binary codes from $ m $-ary $ n $-cubes $ Q^m_n $

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