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- Title
Nonbinary quantum codes from constacyclic codes over polynomial residue rings.
- Authors
Tang, Yongsheng; Yao, Ting; Sun, Zhonghua; Zhu, Shixin; Kai, Xiaoshan
- Abstract
Let R be the polynomial residue ring F q 2 + u F q 2 , where F q 2 is the finite field with q 2 elements, q is a power of a prime p, and u is an indeterminate with u 2 = 0. We introduce a Gray map from R to F q 2 p and study (1 - u) -constacyclic codes over R. It is proved that the image of a (1 - u) -constacyclic code of length n over R under the Gray map is a distance-invariant linear cyclic code of length pn over F q 2. We give some necessary and sufficient conditions for (1 - u) -constacyclic codes over R to be Hermitian dual-containing. In particular, a new class of 2 m -ary quantum codes is obtained via the Gray map and the Hermitian construction from Hermitian dual-containing (1 - u) -constacyclic codes over the ring F 2 2 m + u F 2 2 m .
- Subjects
CYCLIC codes; LINEAR codes; POLYNOMIAL rings; CIPHERS; FINITE fields
- Publication
Quantum Information Processing, 2020, Vol 19, Issue 3, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-020-2584-z