The Weight Enumerator Polynomials of the Lifted Codes of the Projective Solomon-Stiffler Codes

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2024-08-01 DOI:10.1109/TIT.2024.3436923

Minjia Shi;Shitao Li;Tor Helleseth

引用次数: 0

Abstract

Determining the weight distribution of a code is an old and fundamental topic in coding theory that has been thoroughly studied. In 1977, Helleseth, Kløve, and Mykkeltveit presented a weight enumerator polynomial of the lifted code over

${\mathbb {F}}_{q^{\ell } }$

of a q-ary linear code with significant combinatorial properties, which can determine the support weight distribution of this linear code. The Solomon-Stiffler codes are a family of famous Griesmer codes, which were proposed by Solomon and Stiffler in 1965. In this paper, we determine the weight enumerator polynomials of the lifted codes of the projective Solomon-Stiffler codes using some combinatorial properties of subspaces. As a result, we determine the support weight distributions of the projective Solomon-Stiffler codes. In particular, we determine the weight hierarchies of the projective Solomon-Stiffler codes.

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射影索罗门-斯蒂夫勒码的提升码的权数列举多项式

确定编码的权重分布是编码理论中一个古老而基本的课题，已被深入研究过。1977 年，Helleseth、Kløve 和 Mykkeltveit 提出了在 ${{mathbb {F}}_{q^\{ell }$ 上的提升码的权重枚举多项式。}$ 的 qary 线性编码的权重枚举器多项式，它具有重要的组合特性，可以确定该线性编码的支持权重分布。所罗门-斯蒂夫勒编码是著名的格里斯梅尔编码系列，由所罗门和斯蒂夫勒于 1965 年提出。在本文中，我们利用子空间的一些组合性质确定了射影 Solomon-Stiffler 码的提升码的权值枚举多项式。因此，我们确定了射影索罗门-斯蒂夫勒码的支持权重分布。特别是，我们确定了射影索罗门-斯蒂夫勒码的权重等级。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.