Group codes over binary tetrahedral group
Journal of Mathematical Cryptology, 2022 In this article, the group algebra K[T]{\mathcal{K}}\left[{\mathscr{T}}] of the binary tetrahedral group T{\mathscr{T}} over a splitting field K{\mathcal{K}} of T{\mathscr{T}} with char(K)≠2,3{\rm{char}}\left({\mathcal{K}})\ne 2,3 is studied and the ...
Dadhwal Madhu, Pankaj
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Non-binary quantum codes from constacyclic codes over 𝔽q[u1, u2,…,uk]/⟨ui3 = ui, uiuj = ujui⟩
Open Mathematics, 2022 Let q=pmq={p}^{m}, pp be an odd prime, and Rk=Fq[u1,u2,…,uk]/⟨ui3=ui,uiuj=ujui⟩{R}_{k}={{\mathbb{F}}}_{q}\left[{u}_{1},{u}_{2},\ldots ,{u}_{k}]\hspace{-0.08em}\text{/}\hspace{-0.08em}\langle {u}_{i}^{3}={u}_{i},{u}_{i}{u}_{j}={u}_{j}{u}_{i}\rangle ...
Kong Bo, Zheng Xiying
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On Codes Over R and its Bounds of Some kind of Block Repetition Codes in R
InPrime, 2022 This correspondence determines the lower and upper bounds of the covering radius in some kind of block repetition codes over the finite ring R=Z_2 Z_*, where Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v.
P Chella Pandian
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Enumeration of some matrices and free linear codes over commutative finite local rings
Special Matrices, 2021 Let R be a commutative finite local ring. Two enumeration problems over R are presented. We enumerate the matrices over R with a given McCoy rank and a given number of rows of single unit, and the free linear codes over R which have a given rank and a ...
Sirisuk Siripong
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Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields
Special Matrices, 2021 The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽n×n is defined as ℓ1ℓ2· · · ℓn, where ℓj ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero ...
Dukes Peter J., Martínez-Rivera Xavier
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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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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
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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
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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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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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