Symmetry codes over GF(3) and new five-designs

DOI10.1016/0097-3165(72)90088-XzbMath0225.94005OpenAlexW2020908345MaRDI QIDQ2548945

Vera S. Pless

Publication date: 1972

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(72)90088-x

Mathematics Subject Classification ID

Related Items (41)

Unnamed Item ⋮ Algebraic theory of block codes detecting independent errors ⋮ Quadratic spaces over finite fields and codes ⋮ Hadamard matrices of order 36 formed by codewords in some ternary self-dual codes ⋮ Center sets and ternary codes ⋮ Symmetry codes over GF(3) ⋮ In memoriam. A tribute to Vera Pless (1931--2020) ⋮ Extremal ternary self-dual codes of length 36 and symmetric 2-(36, 15, 6) designs with an automorphism of order 2 ⋮ Distance-regular graphs and new block designs obtained from the Mathieu groups ⋮ Experimental constructions of self-dual codes ⋮ A good method of combining codes ⋮ The family of t-designs. Part I ⋮ Block designs from self-dual codes obtained from Paley designs and Paley graphs ⋮ Hadamard matrices of orders 60 and 64 with automorphisms of orders 29 and 31 ⋮ New support 5-designs from lifted linear codes ⋮ Hadamard matrices related to a certain series of ternary self-dual codes ⋮ Semi-automorphisms of Hadamard matrices ⋮ Codes and designs -- existence and uniqueness ⋮ On the existence of extremal Type II ℤ_{2𝕜}-codes ⋮ On the additivity of block designs ⋮ A construction of group divisible designs with block sizes 3 to 7 ⋮ Genetic algorithms in coding theory -- a table for \(A_ 3(n, d)\) ⋮ Symmetry codes and their invariant subcodes ⋮ Contractions of self-orthogonal codes ⋮ On the classification and enumeration of self-dual codes ⋮ Split codes and the Mathieu groups ⋮ Classifications of certain t-designs ⋮ Mutually disjoint designs and new 5-designs derived from groups and codes ⋮ A family of group divisible designs with arbitrary block sizes ⋮ Computational results of duadic double circulant codes ⋮ A class of three-designs ⋮ On circulant self-dual codes over small fields ⋮ Higher power residue codes. ⋮ An infinite class of 5-designs ⋮ Construction of new extremal unimodular lattices ⋮ A survey of constructive coding theory, and a table of binary codes of highest known rate ⋮ Mutually disjoint 5-designs from Pless symmetry codes ⋮ Self-dual codes over chain rings ⋮ An improved upper bound on self-dual codes over finite fields \(\mathrm{GF}(11)\), \(\mathrm{GF}(19)\), and \(\mathrm{GF}(23)\) ⋮ On Pless symmetry codes, ternary QR codes, and related Hadamard matrices and designs ⋮ Quadratic double circulant codes over fields

Cites Work

• Unnamed Item
• Note on the Mathieu group \(M_{12}\)
• Perfect codes and the Mathieu groups
• On t-Designs and Groups
• Power moment identities on weight distributions in error correcting codes
• Disjoint Steiner systems associated with the Mathieu groups
• On the uniqueness of the Golay codes
• New 5-designs
• On a new family of symmetry codes and related new five-designs

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