Results 11 to 20 of about 215 (44)

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, Vandendriessche, Peter   +1 more
core   +2 more sources

Skew cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$

, 2015
In this article, we study skew cyclic codes over ring $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and $v^{3}=v$.
Alahmadi, Adel, Shi, Minjia, Solé, Patrick, Yao, Ting   +3 more
core   +1 more source

Product Construction of Affine Codes

, 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.
Chee, Yeow Meng, Kiah, Han Mao, Purkayastha, Punarbasu, Solé, Patrick   +3 more
core   +1 more source

New extremal binary self-dual codes of length 68 from quadratic residue codes over f_2+uf_2+u^2f_2

, 2013
In this work, quadratic reside codes over the ring F2 +uF2 +u^2F2 with u^3 = u are considered. A duality and distance preserving Gray map from F2 + uF2 + u^2F2 to (F_2)^3 is defined.
Kaya, Abidin, Siap, Irfan, Yildiz, Bahattin   +2 more
core   +1 more source

Skew cyclic codes over 𝔻4R and their applications to DNA codes construction

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
The fundamental aim of this research is to analyze the configuration of 𝔽4R submodules, skew cyclic codes over 𝔽4R and establish their connection with DNA codes, where 𝔽4 is a field of order 4 and R = 𝔽4 + u𝔽4 + v𝔽4 + w𝔽4 with u2 = u, v2 = v, w2 = w, uv =
Rehman Nadeem ur, Ahmad Mohammad Fareed, Azmi Mohd   +2 more
doaj   +1 more source

Two-dimensional cyclic codes over a finite chain ring

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this paper, we have determined the generators and rank of a 2D cyclic code of length mn over a finite chain ring ℛ with residue field 𝔽q, where m is arbitrary and q ≡ 1(mod n).
Garg Disha, Dutt Sucheta
doaj   +1 more source

Further Results on Homogeneous Two-Weight Codes [PDF]

, 2014
The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2].
Honold, Thomas
core  

Every Binary Self-Dual Code Arises From Hilbert Symbols

, 2012
In this paper we construct binary self-dual codes using the \'etale cohomology of $\mathbb{Z}/2$ on the spectra of rings of $S$-integers of global fields.
Chinburg, Ted, Zhang, Ying
core   +1 more source

Graph-Based Classification of Self-Dual Additive Codes over Finite Fields

, 2008
Quantum stabilizer states over GF(m) can be represented as self-dual additive codes over GF(m^2). These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence ...
Danielsen, Lars Eirik
core   +4 more sources

New extremal binary self-dual codes of length 68 via short kharaghani array over f_2 + uf_2 [PDF]

, 2016
In this work, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and a variation of it. These are applicable to any commutative Frobenius ring.
Kaya, Abidin
core   +2 more sources