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Search: WFRF:(Hessler Martin) > (2006)

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1.
  • Heden, Olof, et al. (author)
  • On the classification of perfect codes : side class structures
  • 2006
  • In: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 40:3, s. 319-333
  • Journal article (peer-reviewed)abstract
    • The side class structure of a perfect 1-error correcting binary code (hereafter referred to as a perfect code) C describes the linear relations between the coset representatives of the kernel of C. Two perfect codes C and C' are linearly equivalent if there exists a non-singular matrix A such that AC = C' where C and C' are matrices with the code words of C and C' as columns. Hessler proved that the perfect codes C and C' are linearly equivalent if and only if they have isomorphic side class structures. The aim of this paper is to describe all side class structures. It is shown that the transpose of any side class structure is the dual of a subspace of the kernel of some perfect code and vice versa; any dual of a subspace of a kernel of some perfect code is the transpose of the side class structure of some perfect code. The conclusion is that for classification purposes of perfect codes it is sufficient to find the family of all kernels of perfect codes.
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2.
  • Hessler, Martin (author)
  • Perfect codes as isomorphic spaces
  • 2006
  • In: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 306:16, s. 1981-1987
  • Journal article (peer-reviewed)abstract
    • Linear equivalence between perfect codes is defined. This definition gives the concept of general perfect 1-error correcting binary codes. These are defined as 1-error correcting perfect binary codes, with the difference that the set of errors is not the set of weight one words, instead any set with cardinality n and full rank is allowed. The side class structure defines the restrictions on the subspace of any general 1-error correcting perfect binary code. Every linear equivalence class will contain all codes with the same length, rank and dimension of kernel and all codes in the linear equivalence class will have isomorphic side class structures.
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  • Result 1-2 of 2
Type of publication
journal article (2)
Type of content
peer-reviewed (2)
Author/Editor
Hessler, Martin (2)
Heden, Olof (1)
University
Royal Institute of Technology (2)
Linköping University (2)
Language
English (2)
Research subject (UKÄ/SCB)
Natural sciences (1)
Year
2006 (2)Undo refine

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