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首页> 外文期刊>Designs, Codes and Crytography >Multiple blocking sets in finite projective spaces and improvements to the Griesmer bound for linear codes
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Multiple blocking sets in finite projective spaces and improvements to the Griesmer bound for linear codes

机译：有限射影空间中的多个分块集以及对线性代码的Griesmer界的改进

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摘要

Belov, Logachev and Sandimirov construct linear codes of minimum distance d for roughly 1/q~(k/2) of the values of d < q~(k-1). In this article we shall prove that, for q = p prime and roughly 3/8-th's of the values of d < q~(k-1), there is no linear code meeting the Griesmer bound. This result uses Blokhuis' theorem on the size of a t-fold blocking set in PG(2, p), p prime, which we generalise to higher dimensions. We also give more general lower bounds on the size of a t-fold blocking set in PG(δ, q), for arbitrary q and δ ≥ 3. It is known that from a linear code of dimension k with minimum distance d < q~(k-1) that meets the Griesmer bound one can construct a t-fold blocking set of PG(k - 1,q). Here, we calculate explicit formulas relating t and d. Finally we show, using the generalised version of Blokhuis' theorem, that nearly all linear codes over F_p of dimension k with minimum distance d < q~(k-1), which meet the Griesmer bound, have codewords of weight at least d + p in subcodes, which contain codewords satisfying certain hypotheses on their supports.
机译：Belov，Logachev和Sandimirov为d

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