New non-binary quantum codes from skew constacyclic and additive skew constacyclic codes
Department of Mathematics, Indian Institute of Technology Patna, 801 106, Patna, India
Accepted: 25 January 2022
Published online: 8 February 2022
This paper discusses the structure of skew constacyclic codes and their Hermitian dual over finite commutative non-chain ring where q is odd prime power. We also extend our study over mixed alphabet codes. First, we find necessary and sufficient conditions for skew constacyclic codes to contain their duals over and . Then, a Gray map , is defined, and with the help of this map, we also define another Gray map and prove that both maps are -linear Hermitian dual preserving. Finally, by applying Hermitian construction on dual-containing skew constacyclic codes, we construct many new quantum codes that improve the best-known parameters.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022