arXiv subjects

Long B. Tran

Publications and source records attributed to Long B. Tran.

2 recordsLinked to original sources

arXiv2026

New Codes from Cyclic and Negacyclic Codes of Even Length over $\mathbb{Z}_4$

This paper uses theoretical results previously established in the literature to design search algorithms to find new linear codes over $\mathbb{Z}_4$ from cyclic and negacyclic codes of even length. As a result of these searches, we have found 2500 new cyclic codes and 730 negacyclic codes. These new codes exhibit improved parameters compared to previously known codes. Additionally, we have obtained binary quantum codes with good parameters from such $\mathbb{Z}_4$ codes.

cs.IT↗

arXiv2024

Elementary Constructions of Best Known Quantum Codes

Recently, many good quantum codes over various finite fields $F_q$ have been constructed from codes over extension rings or mixed alphabet rings via some version of a Gray map. We show that most of these codes can be obtained more directly from cyclic codes or their generalizations over $F_q$. Unless explicit benefits are demonstrated for the indirect approach, we believe that direct and more elementary methods should be preferred.

cs.IT↗