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Problemy Peredachi Informatsii, 1992, Volume 28, Issue 1, Pages 39–51
(Mi ppi1335)
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This article is cited in 1 scientific paper (total in 1 paper)
Information Theory and Coding Theory
New Lower Bounds for Minimum Distance of Linear Quasi-Cyclic and Almost Linear Cyclic Codes
V. V. Chepyzhov
Abstract:
New lower bounds are derived for the minimum distance of linear $(np,kp)$ quasi-cyclic codes over arbitrary fields $GF(q)$ for transmission rate $R=k/n$ and for almost linear cyclic codes of length $p$ over nonprime fields $GF(q^n)$ for transmission rate $R=k/n$, where $p$ is any prime number. It is not assumed that $q$ is a primitive root modulo $p$. This result makes it possible to establish the asymptotic attainability of the corresponding Gilbert–Varshamov bounds by quasi-cyclic and almost linear cyclic codes with the indicated characteristics for almost all prime numbers $p$.
Received: 26.03.1991
Citation:
V. V. Chepyzhov, “New Lower Bounds for Minimum Distance of Linear Quasi-Cyclic and Almost Linear Cyclic Codes”, Probl. Peredachi Inf., 28:1 (1992), 39–51; Problems Inform. Transmission, 28:1 (1992), 33–44
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https://www.mathnet.ru/eng/ppi1335 https://www.mathnet.ru/eng/ppi/v28/i1/p39
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Abstract page: | 297 | Full-text PDF : | 158 |
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