Qadratic residue codes over Fp+uFp+vFP*

被引：0
作者：
Pathak, Sachin [1 ]
Ghosh, Gobinda [1 ]
Yadav, Bhanu P. [1 ]
Upadhyay, Ashish K. [2 ]
机构：
[1] Indian Inst Technol Patna, Dept Math, Patna 801103, Bihar, India
[2] Banaras Hindu Univ, Dept Math, Varanasi 221005, Uttar Pradesh, India
来源：
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2021年 / 14卷 / 10期
关键词：
QR codes; cyclic codes; dual codes; generating idempotents;
D O I：
10.1142/S1793557121501746
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study quadratic residue (QR) codes of prime length q over the ring R = F-p + uF(p) + vF(p) with u(2) = u, v(2) = v and uv = vu = 0, where p and q are distinct odd prime numbers. We analyze some basic properties of cyclic codes of length n over R, we define QR codes by their generating idempotents. Further, we discuss the extended QR codes. We present a considerable number of good p-ary codes as Gray images of QR codes over F-p + uF(p) + vF(p) by considering the case when p is an odd prime.
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页数：10
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