共查询到15条相似文献,搜索用时 62 毫秒
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研究了环F4+uF4与域F4上的线性码,利用环F4+uF4上码C的Gray重量wG,Gray距离d G和(F4+uF4)n到F4 2n的Gray映射φ,证明了环F4+uF4上线性码C及其对偶码的Gray像φ(C)为F4上的线性码和对偶且dH G(φ(C))dG(C)。同时,给出了F4+uF4上循环码C的Gray像φ(C)为F4上的2-拟循环码。 相似文献
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环F2+uF2上线性码及其对偶码的二元象 总被引:1,自引:0,他引:1
利用环F2+uF2上线性码C的生成矩阵给出了码C的对偶码C^┴及其Gray象Ф(C)的生成矩阵,证明了环F2+uF2上线性码及其对偶码的Gray象仍是对偶码。并由此给出了一个环F2+uF2如上线性码为自对偶码的充要条件。 相似文献
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在有限环F2+uF2+…+u^k F2与F2之间定义一个新的Gray映射,证明了该映射是距离保持映射。考察了F2+uF2+…+u^k F2环上循环码,得到了F2+uF2+…+u^k F2环上循环码的生成多项式。最后,证明了F2+uF2+…+u^k F2环上循环码在新定义的Gray映射下的像是F2上的准循环码。 相似文献
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The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code. 相似文献
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The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code. 相似文献
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SHI Minjia 《电子学报:英文版》2014,(4):773-777
This paper is devoted to the study of con- stacyclic codes over a non-chain ring R. The generator polynomials of all constacyclic codes over R are characterized and their dual codes are also determined. We also introduce a Gray map. It is proved that the image of a vconstacyclic code of length n over R under the Gray map is a cyclic code of length 2n over a field with p elements, where p is odd prime. Moreover, we obtain a substantial number of optimal p-ary linear (cyclic) codes, in terms of their parameters, via the Gray map. 相似文献
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We study skew cyclic codes over a non-chain ring, which generalizes our previous results in IEICE Trans. on Fundamentals of Electronic Communications and Computer Sciences, 2015. We describe generator polynomi-als of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over the ring by a decomposition theorem. The generator polynomial of the dual code of a skew cyclic code are obtained. Moreover, the idempotent generators of skew cyclic codes are consid-ered. Some examples are also presented to illustrate the discussed results. 相似文献