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The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces

Frédéric A. B. Edoukou (2009)

Journal de Théorie des Nombres de Bordeaux

We study the functional codes C 2 ( X ) defined on a projective algebraic variety X , in the case where X ⊂ ℙ 3 ( 𝔽 q ) is a non-degenerate Hermitian surface. We first give some bounds for # X Z ( 𝒬 ) ( 𝔽 q ) , which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code C 2 ( X ) .

Uniformly bounded duplication codes

Peter Leupold, Victor Mitrana (2007)

RAIRO - Theoretical Informatics and Applications

Duplication is the replacement of a factor w within a word by ww. This operation can be used iteratively to generate languages starting from words or sets of words. By undoing duplications, one can eventually reach a square-free word, the original word's duplication root. The duplication root is unique, if the length of duplications is fixed. Based on these unique roots we define the concept of duplication code. Elementary properties are stated, then the conditions under which infinite duplication...

Universal codes and unimodular lattices

Robin Chapman, Patrick Solé (1996)

Journal de théorie des nombres de Bordeaux

Binary quadratic residue codes of length p + 1 produce via construction B and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction A modulo 4 . We prove in a direct way the equivalence of these two constructions for p ≤ 31 . In dimension 32, we obtain an extremal lattice of type II not isometric to the Barnes-Wall lattice B W 32 . The equivalence between construction B modulo 4 plus density doubling and construction...

What is Q-extension?

Bouyukliev, Iliya (2007)

Serdica Journal of Computing

In this paper we present a developed software in the area of Coding Theory. Using it, codes with given properties can be classified. A part of this software can be used also for investigations (isomorphisms, automorphism groups) of other discrete structures-combinatorial designs, Hadamard matrices, bipartite graphs etc.

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