On Higher Weights and Code Existence

机译：关于更高的权重和代码存在

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Several open questions in coding theory relate to non-existence or construction of certain optimal codes. Many previous problems of this kind have been solved by studying possible weight enumerators. A couple of authors in this decade have proposed using higher weights (generalised Hamming weights) to a similar effect. In this paper we suggest one approach based on the weight hierarchy, and it allows us to conduct an extremely rapid computer search to prove that there are exactly two inequivalent [36, 8,16] codes. The technique can also be used to gain new information about the weight hierarchy of the putative [72,36,16] code, but not yet enough to say if it exists or not.

机译：编码理论中的几个悬而未决的问题与某些最优代码的不存在或构造有关。通过研究可能的重量枚举器已经解决了许多以前的此类问题。在这十年中，有两位作者提出使用更高的权重（广义汉明权重）来达到类似的效果。在本文中，我们提出了一种基于权重层次结构的方法，它使我们能够进行非常快速的计算机搜索，以证明确实存在两个不等价的[36，8,16]码。该技术还可以用于获取有关推定的[72,36,16]代码权重层次的新信息，但还不足以说出它是否存在。

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来源
《Cryptography and coding》|2009年|P.56-64|共9页
会议地点 Cirencester(GB);Cirencester(GB)
作者
Hans Georg Schaathun;
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作者单位

University of Surrey Department of Computing GU2 7XH Guildford, Surrey;

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原文格式 PDF
正文语种 eng
中图分类密码的编码与译码;
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1. On the existence of perfect linear codes over Z_4 with respect to homogeneous weight [J] . M. Ozen, V. Siap Applied mathematical sciences . 2012,第41a44期

机译：关于齐次权重在Z_4上存在完美线性码
2. Linear codes over F_3 + uF_3 + u~2F_3: MacWilliams identities, optimal ternary codes from one-Lee weight codes and two-Lee weight codes [J] . Minjia Shi, Dandan Wang, Patrick Solé Journal of Applied Mathematics and Computing . 2016,第1a2期

机译：F_3 + uF_3 + u〜2F_3上的线性代码：MacWilliams身份，单李权重代码和两李权重代码的最佳三元代码
3. NON-EXISTENCE OF A TERNARY CONSTANT WEIGHT (16,5,15;2048) DIAMETER PERFECT CODE [J] . Krotov Denis S., Ostergard Patric R. J., Pottonen Olli Advances in mathematics of communications . 2016,第2期

机译：三重常数（16,5,15; 2048）的完美代码不存在
4. On Higher Weights and Code Existence [C] . Hans Georg Schaathun IMA International Conference on Cryptography and Coding . 2009

机译：在更高的权重和代码存在上
5. On p-adic estimates of weights in Abelian codes over Galois rings [D] . Katz, Daniel J. 2005

机译：关于Galois环上Abelian编码中权重的p-adic估计
6. Motor learning reveals the existence of multiple codes for movement planning [O] . Todd E. Hudson, Michael S. Landy -1

机译：运动学习揭示了运动计划的多个代码的存在
7. A note on the existence of perfect constant weight codes [O] . Roos C. 1983

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8. Existence and Non-Existence of Finitary Codings for a Class of Random Fields.211 Probability, Networks and Algorithms [R] . van den Berg, J., Steif, J. E. 1998

机译：一类随机场的有理数的存在性和不存在性.111概率，网络和算法

On Higher Weights and Code Existence

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