Skew constacyclic codes over finite commutative semi-simple rings
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초록
This paper investigates skew $\Theta$-$\lambda$-constacyclic codes over $R={\bf F}_0\oplus {\bf F}_1 \oplus \cdots \oplus {\bf F}_{k-1}$, where ${\bf F}_i$'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 $R$.
Abstract
This paper investigates skew $\Theta$-$\lambda$-constacyclic codes over $R={\bf F}_0\oplus {\bf F}_1 \oplus \cdots \oplus {\bf F}_{k-1}$, where ${\bf F}_i$'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 $R$.
참고문헌 (14)
- M. M. Al-Ashker, "Simplex codes over the ring F2 +uF2", Arab. J. Sci. Eng. Sect. A Sci, 30(2), pp.277~285 (2005)
- A. Bonnecaze, "Cyclic codes and self-dual codes over F2 + uF2", IEEE Trans. Inform. Theory, 45(4), pp.1250~1255 (1999)
- D. Boucher, "Skew-cyclic codes", Appl. Algebra Engrg. Comm. Comput, 18(4), pp.379~389 (2007)
- D. Boucher, "Skew constacyclic codes over Galois rings", Adv. Math. Commun, 2(3), pp.273~292 (2008)
- D. Boucher, "Coding with skew polynomial rings", J. Symbolic Comput, 44(12), pp.1644~1656 (2009)
- D. Boucher, "Cryptography and coding", pp.230~243 (2011), Springer
- D. Boucher, "Self-dual skew codes and factorization of skew polynomials", J. Symbolic Com-put, 60, pp.47~61 (2014)
- H. Q. Dinh, "On repeated-root constacyclic codes of length 4ps", Asian-Eur. J. Math, 6(2), pp.25~ (2013)
- H. Q. Dinh, "Skew constacyclic codes over finite elds and finite chain rings", Math. Probl. Eng, 2016, pp.17~ (2016)
- H. Q. Dinh, "Constacyclic codes over finite commutative semi-simple rings", Finite Fields Appl, 45, pp.1~18 (2017)
- Jian Gao, "SKEW CYCLIC CODES OVER Fp + vFp", Journal of Applied Mathematics and Informatics, 31(3), pp.337~342 (2013), 한국전산응용수학회
- J. Gao, "A Chinese remainder theorem approach to skew gener-alized quasi-cyclic codes over finite fields", Cryptogr. Commun, 8(1), pp.51~66 (2016)
- F. Gursoy, "Construction of skew cyclic codes over Fq +vFq", Adv. Math. Commun, 8(3), pp.313~322 (2014)
- S. Jitman, "Skew constacyclic codes over finite chain rings", Adv. Math. Commun, 6(1), pp.39~63 (2012)