arXiv subjects

Satanan Thipworawimon

Publications and source records attributed to Satanan Thipworawimon.

2 recordsLinked to original sources

arXiv2019

Hulls of Linear Codes Revisited with Applications

Hulls of linear codes have been of interest and extensively studied due to their rich algebraic structures and wide applications. In this paper, alternative characterizations of hulls of linear codes are given as well as their applications. Properties of hulls of linear codes are given in terms of their Gramians of their generator and parity-check matrices. Moreover, it is show that the Gramian of a generator matrix of every linear code over a finite field of odd characteristic is diagonalizable. Subsequently, it is shown that a linear code over a finite field of odd characteristic is complementary dual if and only if it has an orthogonal basis. Based on this characterization, constructions of good entanglement-assisted quantum error-correcting codes are provided.

cs.IT↗

arXiv2019

Linear $\ell$-Intersection Pairs of Codes and Their Applications

In this paper, a linear $\ell$-intersection pair of codes is introduced as a generalization of linear complementary pairs of codes. Two linear codes are said to be a linear $\ell$-intersection pair if their intersection has dimension $\ell$. Characterizations and constructions of such pairs of codes are given in terms of the corresponding generator and parity-check matrices. Linear $\ell$-intersection pairs of MDS codes over $\mathbb{F}_q$ of length up to $q+1$ are given for all possible parameters. As an application, linear $\ell$-intersection pairs of codes are used to construct entanglement-assisted quantum error correcting codes. This provides a large number of new MDS entanglement-assisted quantum error correcting codes.

cs.IT↗