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Displaying 1 – 20 of 76

$2$ -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 note on codes and kets.

Caragiu, Mihai (2005)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

A note on weight enumerators of linear self-dual codes.

Lomadze, N. (1998)

Georgian Mathematical Journal

A reversible code over $G F (q)$

Sunil Kumar Muttoo, Shankar Lal (1986)

Kybernetika

Algorithme de Brill-Noether et codes de Goppa

D. Le Brigand, J.J. Risler (1988)

Bulletin de la Société Mathématique de France

Alon-Babai-Suzuki's conjecture related to binary codes in nonmodular version.

Hwang, K.-W., Kim, T., Jang, L.C., Kim, P., Sohn, Gyoyong (2010)

Journal of Inequalities and Applications [electronic only]

An asymptotic Gilbert-Varshamov bound for $(T, M, S)$ -nets.

Bierbrauer, Jürgen, Schmid, Wolfgang Ch. (2005)

Integers

An extremal doubly even self-dual code of length 112.

Harada, Masaaki (2008)

The Electronic Journal of Combinatorics [electronic only]

An Improvement to the Achievement of the Griesmer Bound

Hamada, Noboru, Maruta, Tatsuya (2010)

Serdica Journal of Computing

We denoted by nq(k, d), the smallest value of n for which an [n, k, d]q code exists for given q, k, d. Since nq(k, d) = gq(k, d) for all d ≥ dk + 1 for q ≥ k ≥ 3, it is a natural question whether the Griesmer bound is attained or not for d = dk , where gq(k, d) = ∑[d/q^i], i=0,...,k-1, dk = (k − 2)q^(k−1) − (k − 1)q^(k−2). It was shown by Dodunekov [2] and Maruta [9], [10] that there is no [gq(k, dk ), k, dk ]q code for q ≥ k, k = 3, 4, 5 and for q ≥ 2k − 3, k ≥ 6. The purpose of this paper...

Bezpečnostní kódy v železničních zabezpečovacích zařízeních

Lucie Kárná, Štěpán Klapka (2013)

Pokroky matematiky, fyziky a astronomie

Binary codes and partial permutation decoding sets from the odd graphs

Washiela Fish, Roland Fray, Eric Mwambene (2014)

Open Mathematics

For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, the set of all k-subsets of Ω = 1, 2, …, 2k +1, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k)...

Circuit lower bounds and linear codes.

Paturi, R., Pudlák, P. (2004)

Zapiski Nauchnykh Seminarov POMI

Classification of generalized Hadamard matrices $H (6, 3)$ and quaternary Hermitian self-dual codes of length 18.

Harada, Masaaki, Lam, Clement, Munemasa, Akihiro, Tonchev, Vladimir D. (2010)

The Electronic Journal of Combinatorics [electronic only]

Codes and designs from triangular graphs and their line graphs

Washiela Fish, Khumbo Kumwenda, Eric Mwambene (2011)

Open Mathematics

For any prime p, we consider p-ary linear codes obtained from the span over $𝔽_{p}$ p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.

Codes and projective multisets.

Dodunekov, Stefan, Simonis, Juriaan (1998)

The Electronic Journal of Combinatorics [electronic only]

Codes correcteurs d'erreurs.

Francois Sigrist (1993)

Elemente der Mathematik

Codes de Goppa

Jean-Francis MICHON (1983/1984)

Seminaire de Théorie des Nombres de Bordeaux

Colorings and nowhere-zero flows of graphs in terms of Berlekamp's switching game.

Schauz, Uwe (2011)

The Electronic Journal of Combinatorics [electronic only]

Combinatorial aspects of code loops

Petr Vojtěchovský (2000)

Commentationes Mathematicae Universitatis Carolinae

The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T. Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E. Goodaire contained in [2]. Within this paper, we focus on their combinatorial construction and prove...

Completing codes

A. Restivo, S. Salemi, T. Sportelli (1989)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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