{"title":"Griesmer Type Bounds for Nonlinear Codes and Their Applications","authors":"Xu Pan;Hao Chen;Hongwei Liu;Shanxiang Lyu","doi":"10.1109/TIT.2025.3538921","DOIUrl":null,"url":null,"abstract":"In this paper, we propose three Griesmer type bounds for the minimum Hamming weight of complementary codes of linear codes. Infinite families of complementary codes meeting the three Griesmer type bounds are given to show these bounds are tight. The Griesmer type bounds proposed in this paper are significantly stronger than the classical Griesmer bound for linear codes. As a by-product, we construct some optimal few-weight codes and determine their weight distributions. As an application, Griesmer type bounds for the column distance of convolutional codes are presented. These Griesmer type bounds are stronger than the Singleton bound for convolutional codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 4","pages":"2550-2563"},"PeriodicalIF":2.9000,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Information Theory","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10873015/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose three Griesmer type bounds for the minimum Hamming weight of complementary codes of linear codes. Infinite families of complementary codes meeting the three Griesmer type bounds are given to show these bounds are tight. The Griesmer type bounds proposed in this paper are significantly stronger than the classical Griesmer bound for linear codes. As a by-product, we construct some optimal few-weight codes and determine their weight distributions. As an application, Griesmer type bounds for the column distance of convolutional codes are presented. These Griesmer type bounds are stronger than the Singleton bound for convolutional codes.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
