Results 1 to 10 of about 164 (43)
Product Construction of Affine Codes
SIAM Journal on Discrete Mathematics, 2015 Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of binary linear codes.
Yeow Meng Chee +2 more
exaly +3 more sources
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established ...
Castillo-Guillén C. A. +1 more
doaj +1 more source
Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 Let q be a power of prime p. In this article, we investigate the reversible cyclic codes of arbitrary length n over the ring R = 𝔽q +u𝔽q + u2𝔽q, where u3 = 0 mod q.
Rehman Nadeem ur +2 more
doaj +1 more source
DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established.
Castillo-Guillén C. A. +1 more
doaj +1 more source
Codes parameterized by the edges of a bipartite graph with a perfect matching
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper we study the main characteristics of some evaluation codes parameterized by the edges of a bipartite graph with a perfect matching.
Sarabia Manuel González +1 more
doaj +1 more source
Self-Dual Cyclic Codes Over M2(ℤ4)
Discussiones Mathematicae - General Algebra and Applications, 2022 In this paper, we study the structure of cyclic codes overM2(ℤ4) (the matrix ring of matrices of order 2 over ℤ4), which is perhaps the first time that the ring is considered as a code alphabet.
Bhowmick Sanjit +3 more
doaj +1 more source
On the non-minimality of the largest weight codewords in the binary Reed-Muller codes [PDF]
, 2011 The study of minimal codewords in linear codes was motivated by Massey who described how minimal codewords of a linear code define access structures for secret sharing schemes.
Klein, Andreas, Storme, Leo
core +2 more sources
On the dual code of points and generators on the Hermitian variety H(2n+1,q²) [PDF]
, 2014 We study the dual linear code of points and generators on a non-singular Hermitian variety H(2n + 1, q(2)). We improve the earlier results for n = 2, we solve the minimum distance problem for general n, we classify the n smallest types of code words and ...
De Boeck, Maarten +1 more
core +2 more sources
List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes [PDF]
, 2012 A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are
F. Hernando +15 more
core +5 more sources
Construction of isodual codes from polycirculant matrices
, 2020 Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual.
Shi, Minjia, Sole, Patrick, Xu, Li
core +3 more sources