On Some Classes of Repeated-root Constacyclic Codes of Length a Power of 2 over Galois Rings

Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings

Algebra Colloquium ◽

10.1142/s1005386721000468 ◽

2021 ◽

Vol 28 (04) ◽

pp. 581-600

Author(s):

Hai Q. Dinh ◽

Hualu Liu ◽

Roengchai Tansuchat ◽

Thang M. Vo

Keyword(s):

Finite Field ◽

Galois Ring ◽

Maximum Distance ◽

Galois Rings ◽

Constacyclic Codes ◽

Chain Ring ◽

Negacyclic Codes ◽

Singleton Bound ◽

Maximum Distance Separable ◽

Special Case

Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].

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Skew constacyclic codes over Galois rings

Advances in Mathematics of Communications ◽

10.3934/amc.2008.2.273 ◽

2008 ◽

Vol 2 (3) ◽

pp. 273-292 ◽

Cited By ~ 41

Author(s):

Delphine Boucher ◽

◽

Patrick Solé ◽

Felix Ulmer ◽

Keyword(s):

Galois Rings ◽

Constacyclic Codes

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Some Repeated-Root Constacyclic Codes Over Galois Rings

IEEE Transactions on Information Theory ◽

10.1109/tit.2017.2738627 ◽

2017 ◽

Vol 63 (10) ◽

pp. 6247-6255 ◽

Cited By ~ 1

Author(s):

Hongwei Liu ◽

Youcef Maouche

Keyword(s):

Galois Rings ◽

Constacyclic Codes

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On structure and distances of some classes of repeated-root constacyclic codes over Galois rings

Finite Fields and Their Applications ◽

10.1016/j.ffa.2016.09.004 ◽

2017 ◽

Vol 43 ◽

pp. 86-105 ◽

Cited By ~ 3

Author(s):

Hai Q. Dinh ◽

Hongwei Liu ◽

Xiu-sheng Liu ◽

Songsak Sriboonchitta

Keyword(s):

Galois Rings ◽

Constacyclic Codes

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Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

Finite Fields and Their Applications ◽

10.1016/j.ffa.2012.10.002 ◽

2013 ◽

Vol 19 (1) ◽

pp. 16-38 ◽

Cited By ~ 19

Author(s):

Sergio R. López-Permouth ◽

Hakan Özadam ◽

Ferruh Özbudak ◽

Steve Szabo

Keyword(s):

Galois Rings ◽

Constacyclic Codes

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(uλ-1)-constacyclic Codes of Arbitrary Lengths over the Ring Fq+uFq+…+uk-1Fq

JOURNAL OF ELECTRONICS INFORMATION TECHNOLOGY ◽

10.3724/sp.j.1146.2012.01257 ◽

2014 ◽

Vol 35 (5) ◽

pp. 1044-1048 ◽

Cited By ~ 1

Author(s):

Ping Li ◽

Shi-xin Zhu ◽

Xiao-shan Kai

Keyword(s):

Constacyclic Codes

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A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

Filomat ◽

10.2298/fil1908237i ◽

2019 ◽

Vol 33 (8) ◽

pp. 2237-2248 ◽

Cited By ~ 1

Author(s):

Habibul Islam ◽

Om Prakash

Keyword(s):

Cyclic Codes ◽

Constacyclic Codes ◽

Gray Maps ◽

Permutation Equivalent ◽

Quasi Cyclic 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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