【24h】

Recursive MDS-codes and Pseudogeometries

机译:递归MDS代码和伪几何

获取原文

摘要

In the notion of a recursive code was introduced and some constructions of recursive MDS codes were proposed. The main result was that for any q is not an element of {2,6}(except possibly q∈{14,18,26,42} there exists a recursive MDS-code in an alphabet of q elements of length 4 and combinatorial dimension 2 (i.e. a recursive[4,2,3]_q-code). One of the constructions we used there was that of pseudogeometries; it enabled us to show that for any q > 126 (except possibly q = 164) there exists a recursive[4,2,3]_q-code that contains all the "constants". One part of the present note is the further application of the pseudogeometry construction which shows that for any q > 164 (resp. q > 26644) there exists a recursive[7,2,6]_q-code (resp.[13,2,12]_q-code) containing "constants". Another result presented here is a negative one: we show that there is no nontrivial pseudogeometry consisting of 14,18,26or42 points with no lines of order2,3,4or6, so the pseudogeometry construction cannot be applied for settling the question mentioned in the above. In both cases the usage of computer is essential.
机译:介绍了递归代码的概念,并提出了递归MDS代码的一些构造。主要结果是,对于任何q都不是{2,6}的元素(可能q∈{14,18,26,42}除外,在长度为4且组合为q的q个元素的字母中存在一个递归MDS代码)维度2(即递归[4,2,3] _q代码)我们使用的一种构造是伪几何;它使我们能够证明对于任何q> 126(可能q = 164除外),都存在包含所有“常量”的递归[4,2,3] _q代码。本说明的一部分是伪几何构造的进一步应用,该构造表明对于任何q> 164(q> 26644)存在一个包含“常量”的递归[7,2,6] _q代码(resp。[13,2,12] _q代码),此处给出的另一个结果是负数:我们证明不存在由非平凡的伪几何组成的14、18、26或42个点的第2、3、4或6阶没有线,因此伪几何构造不能用于解决上述问题,在这两种情况下,使用计算机都是必不可少的。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号