Primitive idempotent tables of cyclic and constacyclic codes

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

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A new family of EAQMDS codes constructed from constacyclic codes

Designs Codes and Cryptography ◽

10.1007/s10623-021-00908-1 ◽

2021 ◽

Author(s):

Xiaojing Chen ◽

Shixin Zhu ◽

Wan Jiang ◽

Gaojun Luo

Keyword(s):

Constacyclic Codes ◽

New Family

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Repeated-Root Constacyclic Codes with Pair-Metric

IEEE Communications Letters ◽

10.1109/lcomm.2020.3041271 ◽

2020 ◽

pp. 1-1

Author(s):

Wei Zhao ◽

Shenghao Yang ◽

Kenneth W. Shum ◽

Xilin Tang

Keyword(s):

Constacyclic Codes

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Constructing MDS Galois self-dual constacyclic codes over finite fields

Discrete Mathematics ◽

10.1016/j.disc.2021.112388 ◽

2021 ◽

Vol 344 (6) ◽

pp. 112388

Author(s):

Jiafu Mi ◽

Xiwang Cao

Keyword(s):

Finite Fields ◽

Constacyclic Codes

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Constacyclic codes over mixed alphabets and their applications in constructing new quantum codes

Quantum Information Processing ◽

10.1007/s11128-021-03083-3 ◽

2021 ◽

Vol 20 (4) ◽

Author(s):

Hai Q. Dinh ◽

Sachin Pathak ◽

Tushar Bag ◽

Ashish Kumar Upadhyay ◽

Woraphon Yamaka

Keyword(s):

Quantum Codes ◽

Constacyclic Codes

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Hamming distances of constacyclic codes of length 3p and optimal codes with respect to the Griesmer and Singleton bounds

Finite Fields and Their Applications ◽

10.1016/j.ffa.2020.101794 ◽

2021 ◽

Vol 70 ◽

pp. 101794

Author(s):

Hai Q. Dinh ◽

Xiaoqiang Wang ◽

Hongwei Liu ◽

Woraphon Yamaka

Keyword(s):

Constacyclic Codes ◽

Optimal Codes

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Primitive idempotent measures on compact semitopological semigroups

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700009198 ◽

1972 ◽

Vol 13 (4) ◽

pp. 451-455 ◽

Cited By ~ 3

Author(s):

Stephen T. L. Choy

Keyword(s):

Partial Order ◽

Partially Ordered Set ◽

Ordered Set ◽

Zero Element ◽

Primitive Idempotent ◽

Natural Partial Order ◽

Partially Ordered

For a semigroup S let I(S) be the set of idempotents in S. A natural partial order of I(S) is defined by e ≦ f if ef = fe = e. An element e in I(S) is called a primitive idempotent if e is a minimal non-zero element of the partially ordered set (I(S), ≦). It is easy to see that an idempotent e in S is primitive if and only if, for any idempotent f in S, f = ef = fe implies f = e or f is the zero element of S. One may also easily verify that an idempotent e is primitive if and only if the only idempotents in eSe are e and the zero element. We let П(S) denote the set of primitive idempotent in S.

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