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- W2227887466 abstract "For the purpose of error correcting linear codes over a finite field GF (q) and fixed dimension k we are interested in codes with high minimum distance d as these allow the correction of up to b(d− 1)/2c errors. On the other hand we are interested in codes with minimum redundancy, i.e. codes of small length n. High minimum distance and small length are controversial goals for the optimization of codes. A linear code C is called optimal in this context if there is no linear code of the same length and higher minimum distance. There are bounds [8] giving limits for the optimal minimum distance of a linear code of fixed length n. There is a lower bound, saying there is a known linear code having this minimum distance. The upper bound is given by theoretic results, for example the Griesmer bound. The known upper bounds are not always exact, meaning that for many parameters [n, k] there are no known codes over GF (q) whose minimal distance is equal to the upper bound. In many cases there is a gap between lower and upper bound. As we are constructing codes we shorten the gap by improving the lower bound. First results obtained with our method were given in [5]. In this paper we report on refinements which allowed the construction of several new codes, in two cases they are optimal." @default.
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- W2227887466 date "2005-01-01" @default.
- W2227887466 modified "2023-09-23" @default.
- W2227887466 title "Construction of (sometimes) optimal linear codes" @default.
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