IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

New Binary Quantum Codes Derived from Quasi-Twisted Codes with Hermitian Inner Product

Yu Yao, Yuena Ma, Jingjie Lv, Hao Song, Qiang Fu

Published May 27, 2021• 6 citations

Abstract

In this paper, a special class of two-generator quasi-twisted (QT) codes with index 2 will be presented. We explore the algebraic structure of the class of QT codes and the form of their Hermitian dual codes. A sufficient condition for self-orthogonality with Hermitian inner product is derived. Using the class of Hermitian self-orthogonal QT codes, we construct two new binary quantum codes [[70, 42, 7]]2, [[78, 30, 10]]2. According to Theorem 6 of Ref.[2], we further can get 9 new binary quantum codes. So a total of 11 new binary quantum codes are obtained and there are 10 quantum codes that can break the quantum Gilbert-Varshamov (GV) bound.

DOI: 10.1587/transfun.2021eal2030

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