The kernel of a binary code containing the zero word partitions the binary coordinates into blocks, two coordinates lying in the same block when every kernel word takes the same value in both, and the \emph{kernel-block rank profile} is the multiset of the dimensions of its linear span punctured on those blocks. For th...
The $\mathbb{Z}_p\mathbb{Z}_{p^2}$-additive codes are subgroups of $\mathbb{Z}_p^{\alpha_1}\times\mathbb{Z}_{p^2}^{\alpha_2}$, and they can be seen as linear codes over $\mathbb{Z}_p$ when $\alpha_2=0$, as $\mathbb{Z}_{p^2}$-additive codes when $\alpha_1=0$, and as $\mathbb{Z}_2\mathbb{Z}_4$-additive codes when $p=2$....
The $\mathbb{Z}_{p^s}$-additive codes are subgroups of $\mathbb{Z}_{p^s}^n$. A $\mathbb{Z}_{p^s}$-linear generalized Hadamard (GH) code is a GH code over $\mathbb{Z}_p$ which is the Gray map image of a $\mathbb{Z}_{p^s}$-additive code. A recursive construction gives such codes $H_p^{t_1,\dots,t_s}$, of type $(n;t_1,\do...
Given a finite Cartesian set $S=X \times Y$ and a decreasing set of monomials $\mathcal M$, we call extremal polynomials for $\mathcal M$ over $S$ those that have the maximum number of zeros in $S$ and whose support belongs to $\mathcal M$. Coordinate factorizations give a family of extremal polynomials; we call them c...
D. K. Bhunia, Eduardo Camps-Moreno, Ignacio García-Marco et al.· 0 citations
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