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    New singly and doubly even binary [72,36,12] self-dual codes from M 2(R)G - group matrix rings

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    Authors
    Korban, Adrian
    Şahinkaya, Serap
    Ustun, Deniz
    Publication Date
    2021-09-17
    
    Metadata
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    Abstract
    In this work, we present a number of generator matrices of the form [ I 2 n | τ 2 ( v ) ] , where I 2 n is the 2 n × 2 n identity matrix, v is an element in the group matrix ring M 2 ( R ) G and where R is a finite commutative Frobenius ring and G is a finite group of order 18. We employ these generator matrices and search for binary [ 72 , 36 , 12 ] self-dual codes directly over the finite field F 2 . As a result, we find 134 Type I and 1 Type II codes of this length, with parameters in their weight enumerators that were not known in the literature before. We tabulate all of our findings.
    Citation
    Korban, A., Şahinkaya, S., & Ustun, D. (2021). New singly and doubly even binary [72,36,12] self-dual codes from M2(R)G - group matrix rings. Finite Fields and their Applications, 76, Article 101924. https://doi.org/10.1016/j.ffa.2021.101924
    Publisher
    Elsevier
    URI
    http://hdl.handle.net/10034/625890
    Type
    article
    Description
    From Elsevier via Jisc Publications Router
    History: accepted 2021-08-26, epub 2021-09-17, issued 2021-12-31
    Article version: AM
    Publication status: Published
    Collections
    Mathematics

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