NEW QUANTUM CODES FROM SKEW CONSTACYCLIC CODES

被引：15
|
作者：
Verma, Ram Krishna [1 ]
Prakash, Om [1 ]
Singh, Ashutosh [1 ]
Islam, Habibul [1 ]
机构：
[1] Indian Inst Technol Patna, Dept Math, Patna 801106, Bihar, India
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2021年
关键词：
Cyclic code; constacyclic code; skew constacyclic code; gray map; quantum code; CYCLIC CODES; CONSTRUCTION;
D O I：
10.3934/amc.2021028
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
finite field with pm elements and R`,m = Fpm [v1, v2, . . . , v`]/(vi2 - 1, vivj - vjvii1 <= i,j <=`. Thus R`,m is a finite commutative non-chain ring of order p2Em with characteristic p. In this paper, we aim to construct quantum codes from skew constacyclic codes over R`,m. First, we discuss the structures of skew constacyclic codes and determine their Euclidean dual codes. Then a relation between these codes and their Euclidean duals has been obtained. Finally, with the help of a duality-preserving Gray map and the CSS construction, many MDS and better non-binary quantum codes are obtained as compared to the best-known quantum codes available in the literature.
引用
收藏
页码：900 / 919
页数：20
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