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Heuristic Algorithms for Constructing Binary Constant Weight Codes

机译：构造二进制恒权码的启发式算法

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Constant weight binary codes are used in a number of applications. Constructions based on mathematical structure are known for many codes. However, heuristic constructions unrelated to any mathematical structure can become of greater importance when the parameters of the code are larger. This paper considers the problem of finding constant weight codes with the maximum number of codewords from a purely algorithmic perspective. A set of heuristic and metaheuristic methods is presented and developed into a variable neighborhood search framework. The proposed method is applied to 383 previously studied cases with lengths between 29 and 63. For these cases it generates 153 new codes, with significantly increased numbers of codewords in comparison with existing constructions. For 10 of these new codes the number of codewords meets a known upper bound, and so these 10 codes are optimal. As well as the ability to generate new best codes, the approach has the advantage that it is a single method capable of addressing many sets of parameters in a uniform way.
机译：恒重二进制代码在许多应用中使用。基于数学结构的构造对于许多代码而言是已知的。但是，当代码的参数较大时，与任何数学结构无关的启发式构造可能会变得更加重要。本文从纯粹算法的角度考虑了寻找具有最大码字数的恒定权重码的问题。提出了一套启发式和元启发式方法，并将其发展为可变邻域搜索框架。该方法适用于383个以前研究过的长度在29到63之间的情况。对于这些情况，它会生成153个新代码，与现有结构相比，代码字的数量大大增加。对于这些新代码中的10个，代码字的数量满足已知的上限，因此这10个代码是最佳的。除了产生新的最佳代码的能力之外，该方法还具有以下优点：它是一种能够以统一的方式处理许多参数集的单一方法。

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