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  • 1.
    Danev, Danyo
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Dodunekov, Stefan
    Bulgarian Academy of Sciences.
    A Family of Ternary Quasi-Perfect BCH Codes2008In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 49, p. 265-271Article in journal (Refereed)
    Abstract [en]

    In this paper we present a family of ternary quasi-perfect BCH codes. These codes are of minimum distance 5 and covering radius 3. The first member of this family is the ternary quadratic-residue code of length 13.

  • 2.
    Heden, Olof
    et al.
    Department of Mathematics, KTH, S-100 44 Stockholm, Sweden.
    Hessler, Martin
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the classification of perfect codes: Side class structures2006In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 40, no 3, p. 319-333Article in journal (Refereed)
    Abstract [en]

    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. © Springer Science + Business Media, LLC 2006.

  • 3.
    Löfvenberg, Jacob
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Information Theory.
    Binary Fingerprinting Codes2005In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 36, no 1, p. 69-81Article in journal (Refereed)
    Abstract [en]

    Three binary fingerprinting code classes with properties similar to codes with the identifiable parent property are proposed. In order to compare such codes a new combinatorial quality measure is introduced. In the case of two cooperating pirates the measure is derived for the proposed codes, upper and lower bounds are constructed and the results of computer searches for good codes in the sense of the quality measure are presented. Some properties of the quality measure are also derived.

  • 4.
    Stokes, Klara
    et al.
    Universitat Rovira i Virgili, Spain.
    Farràs, Oriol
    Universitat Rovira i Virgili, Spain.
    Linear spaces and transversal designs:k-anonymous combinatorial configurations for anonymous database search2012In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 71, no 3, p. 503-524Article in journal (Refereed)
    Abstract [en]

    Anonymous database search protocols allow users to query a database anonymously. This can be achieved by letting the users form a peer-to-peer community and post queries on behalf of each other. In this article we discuss an application of combinatorial configurations (also known as regular and uniform partial linear spaces) to a protocol for anonymous database search, as defining the key-distribution within the user community that implements the protocol. The degree of anonymity that can be provided by the protocol is determined by properties of the neighborhoods and the closed neighborhoods of the points in the combinatorial configuration that is used. Combinatorial configurations with unique neighborhoods or unique closed neighborhoods are described and we show how to attack the protocol if such configurations are used. We apply k-anonymity arguments and present the combinatorial configurations with k-anonymous neighborhoods and with k-anonymous closed neighborhoods. The transversal designs and the linear spaces are presented as optimal configurations among the configurations with k-anonymous neighborhoods and k-anonymous closed neighborhoods, respectively.

  • 5.
    Svanström, Mattias
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering.
    A class of perfect ternary constant-weight codes1999In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 18, no 1-3, p. 223-229Article in journal (Refereed)
    Abstract [en]

    We construct a class of perfect ternary constant-weight codes of length 2(r), weight 2(r)-1 and minimum distance 3. The codes have 2(2r)-1 codewords. The construction is based on combining cosets of binary Hamming codes. As a special case, for r=2 the construction gives the subcode of the tetracode consisting of its nonzero codewords. By shortening the perfect codes, we get further optimal codes.

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