1960/11/01 by J. H. Griesmer, James H. Griesmer · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Algorithm #Arithmetic #Binary code #Binary number #Code (set theory) #Coding theory and cryptography #Combinatorics #Computer science #DNA and Biological Computing #Discrete mathematics #Geometry #Mathematics #Minimum distance #Natural language processing #Order (exchange) #Programming language #Upper and lower bounds #Word (group theory) #Word length #graph theory and CDMA systems
paper · doi:10.1147/rd.45.0532
crossref issued 1960/11/01 · crossref published 1960/11/01 · crossref published-print 1960/11/01 · openalex publication_date 1960/11/01 · crossref created 2010/04/05 · openalex created_date 2025/10/10 · crossref deposited 2025/10/20 · crossref indexed 2026/07/29 · openalex updated_date 2026/08/01
This paper gives two new bounds for the code word length n which is required to obtain a binary group code of order 2kwith mutual distance d between code words. These bounds are compared with previously known bounds, and are shown to improve upon them for certain ranges of k and d. Values of k and d are given for which one of these bounds can actually be achieved; in such cases, the structure of the resulting codes is shown to satisfy a certain condition.