Primitive idempotent tables of cyclic and constacyclic codes
نویسندگان
چکیده
منابع مشابه
Cyclic and constacyclic codes over a non-chain ring
In this study, we consider linear and especially cyclic codes over the non-chain ring Zp[v]/〈v − v〉 where p is a prime. This is a generalization of the case p = 3. Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and p-ary codes and moreover this map enlighte...
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Constacyclic codes may naturally be viewed as objects arising from the cohomological concept of a cocycle. Cohomology theory suggests a transformation which is used to show, under certain circumstances, a cyclic code of length mn over a ring R is isomorphic to the direct sum of m constacyclic codes of length n. In particular this isomorphism holds in many local rings (for example Galois rings) ...
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Symbol-pair code is a new coding framework which is proposed to correct errors in the symbolpair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pairdistance five or six. ...
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In this paper, we make some progress towards a well-known conjecture on the minimum weights of binary cyclic codes with two primitive nonzeros. We also determine the Walsh spectrum of Tr(x) over F2m in the case wherem = 2t, d = 3+2 t+1 and gcd(d, 2−1) = 1.
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In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal parameters. In this light, we propose constructions of families of classical block and convolutional maximum-distance-separable (MDS) constacyclic codes, as we...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2018
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-018-0495-0