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1-perfect codes over self-complementary graphs

Jan Kratochvíl (1985)

Commentationes Mathematicae Universitatis Carolinae

$2$ -modular lattices from ternary codes

Robin Chapman, Steven T. Dougherty, Philippe Gaborit, Patrick Solé (2002)

Journal de théorie des nombres de Bordeaux

The alphabet $𝐅_{3} + v 𝐅_{3}$ where $v^{2} = 1$ is viewed here as a quotient of the ring of integers of $𝐐 (\sqrt{- 2})$ by the ideal (3). Self-dual $𝐅_{3} + v 𝐅_{3}$ codes for the hermitian scalar product give $2$ -modular lattices by construction $A_{K}$ . There is a Gray map which maps self-dual codes for the Euclidean scalar product into Type III codes with a fixed point free involution in their automorphism group. Gleason type theorems for the symmetrized weight enumerators of Euclidean self-dual codes and the length weight enumerator of hermitian self-dual...

A Characterization of Designs Related to the Witt System S(5, 8, 24).

Vladimir D. Tonchev (1986)

Mathematische Zeitschrift

A decoding scheme for the 4-ary lexicodes with $D = 3$ .

Kim, D.G., Kim, H.K. (2002)

International Journal of Mathematics and Mathematical Sciences

A fuzzy commitment scheme with McEliece's cipher.

Ojha, D.B., Sharma, A. (2010)

Surveys in Mathematics and its Applications

A generalized Lloyd theorem and mixed perfect codes.

Olof Heden (1975)

Mathematica Scandinavica

A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. I. General considerations

Štefan Šujan (1982)

Kybernetika

A Loopless Implementation of a Gray Code for Signed Permutations

James Korsh, Paul LaFollette, Seymour Lipschutz (2011)

Publications de l'Institut Mathématique

A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

Hamada, Noboru, Maruta, Tatsuya, Oya, Yusuke (2012)

Serdica Journal of Computing

ACM Computing Classification System (1998): E.4.Let q be a prime or a prime power ≥ 3. The purpose of this paper is to give a necessary and sufficient condition for the existence of an (n, r)-arc in PG(2, q ) for given integers n, r and q using the geometric structure of points and lines in PG(2, q ) for n > r ≥ 3. Using the geometric method and a computer, it is shown that there exists no (34, 3) arc in PG(2, 17), equivalently, there exists no [34, 3, 31] 17 code.This research was partially...

A new lower bound for the football pool problem for $7$ matches

Laurent Habsieger (1996)

Journal de théorie des nombres de Bordeaux

Let $K_{3} (7, 1)$ denote the minimum cardinality of a ternary code of length $7$ and covering radius one. In a previous paper, we improved on the lower bound $K_{3} (7, 1) \geq 147$ by showing that $K_{3} (7, 1) \geq 150$ . In this note, we prove that $K_{3} (7, 1) \geq 153$ .