29,191 research outputs found
Self-Dual codes from (−1,1)-matrices of skew symmetric type
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 Ehlich-
Wojtas’ bound are presented. A necessary and sufficient condition for these codes to be
self-dual is given, and examples are provided for lengths up to 52.Ministerio de Ciencia e Innovación MTM2008-06578Junta de AndalucÃa FQM-016Junta de AndalucÃa P07-FQM-0298
Self-Dual codes from -matrices of skew symmetric type
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 Ehlich-Wojtas' bound are presented. A necessary and sufficient condition
for these codes to be self-dual is given, and examples are provided for lengths
up to 52
Hadamard matrices modulo p and small modular Hadamard matrices
We use modular symmetric designs to study the existence of Hadamard matrices
modulo certain primes. We solve the -modular and -modular versions of
the Hadamard conjecture for all but a finite number of cases. In doing so, we
state a conjecture for a sufficient condition for the existence of a
-modular Hadamard matrix for all but finitely many cases. When is a
primitive root of a prime , we conditionally solve this conjecture and
therefore the -modular version of the Hadamard conjecture for all but
finitely many cases when , and prove a weaker result for
. Finally, we look at constraints on the existence of
-modular Hadamard matrices when the size of the matrix is small compared to
.Comment: 14 pages; to appear in the Journal of Combinatorial Designs; proofs
of Lemma 4.7 and Theorem 5.2 altered in response to referees' comment
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