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Nonbinary quantum codes from constacyclic codes over polynomial residue rings.
- Source :
- Quantum Information Processing; Mar2020, Vol. 19 Issue 3, p1-14, 14p
- Publication Year :
- 2020
-
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 . [ABSTRACT FROM AUTHOR]
- Subjects :
- CYCLIC codes
LINEAR codes
POLYNOMIAL rings
CIPHERS
FINITE fields
Subjects
Details
- Language :
- English
- ISSN :
- 15700755
- Volume :
- 19
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Quantum Information Processing
- Publication Type :
- Academic Journal
- Accession number :
- 141915914
- Full Text :
- https://doi.org/10.1007/s11128-020-2584-z