A large class of MDS linear codes is constructed. These are endowed with an efficient decoding algorithm. Both the definition and design their algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, first part paper develops a direct presentation by means parity-check matrices, rests upon matrix maps manipulations. The somewhat more sophisticated mat...

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

Quantum error-correcting codes have gained prominence since the initial discovery of Shor and Steane. In 1998, Calderbank et al. presented systematic methods to construct binary quantum codes, called stabilizer codes or additive codes, from classical error-correcting codes. Since then the field has made rapid progress, many good binary quantum codes were constructed by using classical error-cor...

In this paper, we give families of self-dual Z4-codes of Type IV-I and Type IV-II generated by conference matrices and skew-Hadamard matrices. Furthermore, we give a family of self-dual Z4-codes of Type IV-I generated by bordered skew-Hadamard matrices.