Results 11 to 20 of about 36,705 (229)
On repeated-root cyclic codes [PDF]
IEEE Transactions on Information Theory, 1991 A parity-check matrix for a q-ary repeated-root cyclic code is derived using the Hasse derivative. Then the minimum distance of a q-ary repeated-root cyclic code is expressed in terms of the minimum distance of a certain simple-root cyclic code. With the help of this result, several binary repeated-root cyclic codes of lengths up to n=62 are shown to ...
G. Castagnoli +3 more
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Quantum Codes Constructed From Repeated-Root Cyclic Codes
Journal of Physics: Conference Series, 2018 In this paper, we use q-cyclotomic cosets modulo n = q − 1 and generator polynomial to describe repeated-root cyclic codes of length N = pαn. We determine the condition under which a repeated-root cyclic code contains its dual code. Then, for q = 2a, we give a class of dual-containing repeated-root cyclic codes.
Ruihu Li +3 more
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On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings [PDF]
Advances in Mathematics of Communications, 2009 Repeated root Cyclic and Negacyclic codes over Galois rings have been studied much less than their simple root counterparts. This situation is beginning to change. For example, repeated root codes of length $p^s$, where $p$ is the characteristic of the alphabet ring, have been studied under some additional hypotheses.
Sergio R. López-Permouth, Steve Szabo
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$b$-symbol distance distribution of repeated-root cyclic codes [PDF]
, 2017 6 ...
Hojjat Mostafanasab +1 more
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Weight Distribution of Repeated-Root Cyclic Codes with Prime Power Lengths [PDF]
, 2023 Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have found broad applications in quantum error-correcting codes, symbol-pair codes, and storage codes.
Wei Zhao +4 more
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Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance [PDF]
Problems of Information Transmission, 2015 The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and
Ulmschneider, Markus, Zeh, Alexander
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Self-dual Repeated Root Cyclic and Negacyclic Codes over Finite Fields [PDF]
2012 IEEE International Symposium on Information Theory Proceedings, 2012 In this paper we investigate repeated root cyclic and negacyclic codes of length $p^rm$ over $\mathbb{F}_{p^s}$ with $(m,p)=1$. In the case $p$ odd, we give necessary and sufficient conditions on the existence of negacyclic self-dual codes. When $m=2m'$ with $m'$ odd, we characterize the codes in terms of their generator polynomials.
Kenza Guenda, T. Aaron Gulliver
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The symbol-pair distance distribution of repeated-root cyclic codes over $\mathbb{F}_{p^m}$ [PDF]
, 2016 Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distances of cyclic codes of length $p^e$ over $\mathbb{F}_{p^m}$.
Shixin Zhu, Zhonghua Sun, Liqi Wang
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On the Hamming distances of repeated-root cyclic codes of length $5p^s$ [PDF]
Discrete Applied Mathematics, 2019 Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let $p$ be a prime with $p\ge 7$. We determine the weight distributions of all cyclic codes of length $5$ over $\f_q$ and the Hamming distances of all repeated-root ...
Xia Li, Qin Yue
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New QEC codes and EAQEC codes from repeated-root cyclic codes of length $2^rp^s$ [PDF]
Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field $\mathbb{F}_{p^m}$.
Lanqiang Li +3 more
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