Skew Cyclic Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$
نویسندگان
چکیده
منابع مشابه
On Skew Cyclic Codes over a Finite Ring
In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
متن کاملOn skew cyclic codes over $F_q+vF_q+v^2F_q$
In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of a skew cyclic code of length $n$ ove...
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In this paper, we study skew cyclic codes over the ring R = Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v, uv = vu, q = p and p is an odd prime. We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.
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In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...
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This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew general...
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ژورنال
عنوان ژورنال: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
سال: 2015
ISSN: 0916-8508,1745-1337
DOI: 10.1587/transfun.e98.a.1845