Fabio Enrique Brochero Martínez

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cs.IT2014

Number of minimal cyclic codes with given length and dimension

F. E. Brochero Martínez

In this article, we count the quantity of minimal cyclic codes of length $n$ and dimension $k$ over a finite field $F_{q}$ , in the case when the prime factors of $n$ satisfy…

cs.IT2014

Explicit factorization of $x^{n} - 1 \in F_{q} [x]$

F. E. Brochero Martínez, C. R. Giraldo Vergara, L. Batista de Oliveira

Let $F_{q}$ be a finite field and $n$ a positive integer. In this article, we prove that, under some conditions on $q$ and $n$ , the polynomial $x^{n} - 1$ can be split into irred…

cs.IT2014

Weight enumerator of some irreducible cyclic codes

F. E. Brochero Martínez, C. R. Giraldo Vergara

In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length $n$ over a finite field $F_{q}$ , in the case which each prime…

Number of minimal cyclic codes with given length and dimension

Explicit factorization of xn−1∈Fq​[x]

Weight enumerator of some irreducible cyclic codes

Explicit factorization of $x^{n} - 1 \in F_{q} [x]$