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首页> 外文期刊>IEEE Transactions on Information Theory >Tilings With amp;formula formulatype='inline'amp; amp;img src='/images/tex/388.gif' alt='n'amp; amp;/formulaamp;-Dimensional Chairs and Their Applications to Asymmetric Codes
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Tilings With amp;formula formulatype='inline'amp; amp;img src='/images/tex/388.gif' alt='n'amp; amp;/formulaamp;-Dimensional Chairs and Their Applications to Asymmetric Codes

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摘要

An $n$-dimensional chair consists of an $n$ -dimensional box from which a smaller $n$-dimensional box is removed. A tiling of an $n$-dimensional chair has two nice applications in some memories using asymmetric codes. The first one is in the design of codes that correct asymmetric errors with limited magnitude. The second one is in the design of $n$ cells $q$ -ary write-once memory codes. We show an equivalence between the design of a tiling with an integer lattice and the design of a tiling from a generalization of splitting (or of Sidon sequences). A tiling of an $n$ -dimensional chair can define a perfect code for correcting asymmetric errors with limited magnitude. We present constructions for such tilings and prove cases where perfect codes for these type of errors do not exist.

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