Results 1 to 10 of about 68 (43)
The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs [PDF]
, 2021 We use known characterizations of generalized Paley graphs which are cartesian decomposable to explicitly compute the spectra of the corresponding associated irreducible cyclic codes. As applications, we give reduction formulas for the number of rational
Podestá, Ricardo A., Videla, Denis E.
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On cyclic algebraic-geometry codes [PDF]
, 2021 In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms.
Cabaña, Gustavo Andrés +3 more
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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
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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
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The conorm code of an AG-code [PDF]
, 2021 Given a suitable extension F′/F of algebraic function fields over a finite field Fq, we introduce the conorm code ConF′/F(C) defined over F′ which is constructed from an algebraic geometry code C defined over F.
Chara, María de Los Ángeles +2 more
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Weight distribution of cyclic codes defined by quadratic forms and related curves [PDF]
, 2021 We consider cyclic codes CL associated to quadratic trace forms inm variables (Formula Presented) determined by a family L of q-linearized polynomials R over Fqm, and three related codes CL,0, CL,1, and CL,2.
Podesta, Ricardo Alberto +1 more
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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
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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
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Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p5 elements (p a prime) and nilpotency index 4 are given.
Castillo-Guillén C. A. +1 more
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Skew Cyclic codes over $\F_q+u\F_q+v\F_q+uv\F_q$ [PDF]
, 2015 In this paper, we study skew cyclic codes over the ring $R=\F_q+u\F_q+v\F_q+uv\F_q$, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a decomposition theorem.
Shi, Minjia, Solé, Patrick, Yao, Ting
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