• 대한수학회보
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• 제56권2호
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• pp.419-437
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• 2019

This paper investigates skew ${\Theta}-{\lambda}$-constacyclic codes over $R=F_0{\oplus}F_1{\oplus}{\cdots}{\oplus}F_{k-1}$, where $F{_i}^{\prime}s$ are finite fields. The structures of skew ${\lambda}$-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew ${\lambda}$-constacyclic codes of arbitrary length are studied under a new definition. We also show that a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over R or a quasi-cyclic code over R.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.337-342
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• 2013

In this paper, we study a special class of linear codes, called skew cyclic codes, over the ring $R=F_p+vF_p$, where $p$ is a prime number and $v^2=v$. We investigate the structural properties of skew polynomial ring $R[x,{\theta}]$ and the set $R[x,{\theta}]/(x^n-1)$. Our results show that these codes are equivalent to either cyclic codes or quasi-cyclic codes. Based on this fact, we give the enumeration of distinct skew cyclic codes over R.

• 대한수학회보
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• 제55권6호
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• pp.1627-1638
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• 2018

In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$, where p is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring (${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$)[$x;{\theta}$] where $v^3=1$ and ${\theta}$ is an ${\mathbb{F}}_p$-automorphism such that ${\theta}(v)=v^2$. We show that when n is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.