Lower bounds on the minimum distance of one-generator quasi-cyclic codes of arbitrary index are introduced, obtained by puncturing and shortening the code at the level of its blocks, and form a nondecreasing chain whose first term is the Jensen bound.
Abstract
We introduce lower bounds on the minimum distance of one-generator quasi-cyclic codes of arbitrary index, obtained by puncturing and shortening the code at the level of its blocks. For balanced codes, these bounds form a nondecreasing chain whose first term is the Jensen bound. We apply these bounds to conduct a computer search and obtain many Hermitian LCD codes with good parameters. Among them there are six codes of length at most 30 which improve the corresponding lower bounds of Araya and Harada. These codes further give maximal-entanglement entanglement-assisted quantum codes, which we compare with the parameters currently recorded in the literature.
We construct quantum codes from codewords of a cyclic code and the minors of a polynomial matrix. The construction uses a two-row, three-column matrix whose minors yield a second matrix satisfying the CSS orthogonality condition. We derive the code dimension from the greatest common divisors of the entries and minors,...
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In this paper, for an odd prime power
q
, we study a class of cyclic codes over
$$\mathbb {F}_q$$
F
q
whose duals have two zeros. Using some results on Gaussian periods of order 2, along with some relations between certain exponential sums and multiple Kloosterman sums, we determine the weight...
Félix Hernández, G. Vega· Applicable Algebra in Engine...· 0 citations
In this paper, we present a method for constructing linear codes derived from book graphs. Applying such a method, we construct binary codes that have the greatest possible minimum distance for their length and dimension by means of the $2$-sum of two equal book graphs. We then utilize matroid and graph theory together...
A. S. Barbosa, Franklin de L. Marquezino, G. L. La Guardia· 0 citations
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