For (n,q)=p(s), where p=ch(F-q), s greater than or equal to 1, V a q(m)-ary repeated-root cyclic code of length n with generator polynomial g(x), we give a partial answer about whether the q-ary image of V is cyclic o...
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For (n,q)=p(s), where p=ch(F-q), s greater than or equal to 1, V a q(m)-ary repeated-root cyclic code of length n with generator polynomial g(x), we give a partial answer about whether the q-ary image of V is cyclic or not with respect to a certain basis for F(q)m over F-q.
Many good quantum error-correcting codes were constructed from cycliccodes. However, it is a difficult problem to determine the true minimum distance of quantum cycliccodes for large length n. In this work, we const...
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Many good quantum error-correcting codes were constructed from cycliccodes. However, it is a difficult problem to determine the true minimum distance of quantum cycliccodes for large length n. In this work, we construct nonbinary quantum cycliccodes and asymmetric quantum cycliccodes that are derived from repeated-root cyclic codes for an arbitrary length p(s), and determine the true minimum distance of all those codes. Some proposed quantum cycliccodes are optimal. Additionally, some proposed asymmetric quantum cycliccodes have better parameters than the ones available in the literature.
Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. Maxim...
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Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that pair distance cannot be improved for given length and code size. The contribution of this paper is twofold. First, we present three lower bounds for the minimum pair distance of constacycliccodes, the first two of which generalize the previously known results due to Cassuto and Blaum (2011) and Kai et al. (2015). The third one exhibits a lower bound for the minimum pair distance of repeated-root cyclic codes. Second, we obtain new MDS symbol-pair codes with minimum pair distance seven and eight through repeated-root cyclic codes.
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