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- W3105341748 abstract "Under research for near sixty years, Bose-$!$Ray-$!$Chaudhuri-$!$Hocquenghem(BCH) codes have played increasingly important roles in many applications such as communication systems, data storage and information security. However, the dimension and minimum distance of BCH codes are seldom solved until now because of their intractable characteristics. The objective of this paper is to study the dimensions of some BCH codes of length $n=2^m+1$ with $m=2t+1$, $4t+2$, $8t+4$ and $mgeq 10$. Some new techniques are employed to investigate coset leaders modulo $n$. For each type of $m$ above, the first five largest coset leaders modulo $n$ are determined, the dimension of some BCH codes of length $n$ with designed distance $delta>2^{lceil frac{m}{2} rceil}$ is presented. These new techniques and results may be helpful to study other families of cyclic codes over finite fields." @default.
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- W3105341748 date "2019-01-01" @default.
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- W3105341748 title "Some binary BCH codes with length n = 2 + 1" @default.
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- W3105341748 doi "https://doi.org/10.1016/j.ffa.2018.09.005" @default.
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