arXiv subjects

M. Villanueva

Publications and source records attributed to M. Villanueva.

3 recordsLinked to original sources

arXiv2012

Self-embeddings of Hamming Steiner triple systems of small order and APN permutations

The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n=2^m-1 for small m, m < 23, is given. As far as we know, for m in {5,7,11,13,17,19}, all given self-embeddings in closed surfaces are new. Moreover, they are cyclic for all m and nonorientable at least for all m < 21. For any non prime m, the nonexistence of such self-embeddings in a closed surface is proven.

cs.IT↗

arXiv2007

Z2Z4-linear codes: generator matrices and duality

A code ${\cal C}$ is $\Z_2\Z_4$-additive if the set of coordinates can be partitioned into two subsets $X$ and $Y$ such that the punctured code of ${\cal C}$ by deleting the coordinates outside $X$ (respectively, $Y$) is a binary linear code (respectively, a quaternary linear code). In this paper $\Z_2\Z_4$-additive codes are studied. Their corresponding binary images, via the Gray map, are $\Z_2\Z_4$-linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes, for these codes the fundamental parameters are found and standard forms for generator and parity check matrices are given. For this, the appropriate inner product is deduced and the concept of duality for $\Z_2\Z_4$-additive codes is defined. Moreover, the parameters of the dual codes are computed. Finally, some conditions for self-duality of $\Z_2\Z_4$-additive codes are given.

cs.IT↗

arXiv2006

On the intersection of additive perfect codes

The intersection problem for additive (extended and non-extended) perfect codes, i.e. which are the possibilities for the number of codewords in the intersection of two additive codes C1 and C2 of the same length, is investigated. Lower and upper bounds for the intersection number are computed and, for any value between these bounds, codes which have this given intersection value are constructed. For all these codes the abelian group structure of the intersection is characterized. The parameters of this abelian group structure corresponding to the intersection codes are computed and lower and upper bounds for these parameters are established. Finally, constructions of codes the intersection of which fits any parameters between these bounds are given.

cs.IT↗