ویراساینس.
سند علمی

Symmetric Designs and Self-dual Codes

ERIC S. LANDER

چکیده

A construction is given for associating to any symmetric (v, k, X) design a self-dual code of length v+ 1 over GF (p), where p is any divisor of the square-free part of k — k. These codes are then used to obtain a substantial strengthening of a result of Hughes on automorphisms of designs. Specifically, suppose a symmetric {v, k, X) design possesses an automorphism a of odd prime order q. If any prime dividing the square-free part of k — A has even (multiplicative) order mod q, then a must fix an odd number of points of the design.

اسناد مشابه

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    مقاله‌ی دسترسی آزاد۲۰۲۲Journal of Algebraic Combinatorics['Sanja Rukavina', 'Vladimir D. Tonchev', '']

    In this note, we report the classification of all symmetric 2-(36, 15, 6) designs that admit an automorphism order 2 and their incidence matrices generate extremal ternary self-dual code. It is shown up to isomorphism, there exists only one such design, having a full group 24, co

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    Abstract. Previously, self-dual codes have been constructed from weighing matrices, and in particular from conference matrices (skew and symmetric). In this paper, codes constructed from matrices of skew symmetric type whose determinants reach the EhlichWojtas’ bound are presente

  • On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24

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    By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5

  • Construction of quasi-cyclic self-dual codes

    سند علمی۲۰۱۲Finite Fields and Their ApplicationsSunghyu Han, Jon-Lark Kim, Heisook Lee, Yoonjin Lee

    There is a one-to-one correspondence between l-quasi-cyclic codes over a finite field Fq and linear codes over a ring R = Fq[Y ]/(Y m − 1). Using this correspondence, we prove that every l-quasi-cyclic self-dual code of length ml over a finite field Fq can be obtained by the buil

  • Some connections between self-dual codes, combinatorial designs and secret sharing schemes

    سند علمی۲۰۱۱Adv. in Math. of Comm.Stefka Bouyuklieva, Zlatko Varbanov

    Some connections between self-dual codes, combinatorial designs and secret-sharing schemes Stefka Bouyuklieva, Zlatko Varbanov Department of Mathematics and Informatics, University of Veliko Tarnovo, Bulgaria In the present work we study a class of singly even self-dual codes wit

  • Quantum self-dual codes and symmetric matrices

    سند علمی۱۹۹۷Vladimir D. Tonchev

    In a recent paper Calderbank, Rains, Shor and Sloane [1] described a method of constructing quantum-error-correcting codes from ordinary binary or quaternary codes that are selforthogonal with respect to a certain inner product. We use this relation to show that a class of binary