Results 1 to 10 of about 281 (29)
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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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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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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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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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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Polynomial evaluation over finite fields: new algorithms and complexity bounds [PDF]
, 2011 An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation in the decoding
A. Borodin +13 more
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Monomial codes seen as invariant subspaces
Open Mathematics, 2017 It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known.
García-Planas María Isabel +2 more
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Constacyclic codes over 𝔽pm[u1, u2,⋯,uk]/〈 ui2 = ui, uiuj = ujui〉
Open Mathematics, 2018 In this paper, we study linear codes over ring Rk = 𝔽pm[u1, u2,⋯,uk]/〈ui2$\begin{array}{} u^{2}_{i} \end{array} $ = ui, uiuj = ujui〉 where k ≥ 1 and 1 ≤ i, j ≤ k.
Zheng Xiying, Kong Bo
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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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