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Title: A class of skew-cyclic codes over ℤ 4 + uℤ 4 with derivation
Authors: Sharma A.
Bhaintwal M.
Published in: Advances in Mathematics of Communications
Abstract: In this paper, we study a class of skew-cyclic codes using a skew polynomial ring over R = ℤ 4 + uℤ 4 ; u 2 = 1, with an automorphism θ and a derivation δ θ . We generalize the notion of cyclic codes to skew-cyclic codes with derivation, and call such codes as δ θ -cyclic codes. Some properties of skew polynomial ring R[x, θ, δ θ ] are presented. A δ θ -cyclic code is proved to be a left R[x, θ, δ θ ]-submodule of R[x,θ,δ 〈xn −1 〉 θ] . The form of a parity-check matrix of a free δ θ -cyclic codes of even length n is presented. These codes are further generalized to double δ θ -cyclic codes over R. We have obtained some new good codes over ℤ 4 via Gray images and residue codes of these codes. The new codes obtained have been reported and added to the database of ℤ 4 -codes [2]. © 2018 AIMS.
Citation: Advances in Mathematics of Communications (2018), 12(4): 723-739
Issue Date: 2018
Publisher: American Institute of Mathematical Sciences
Keywords: Automorphisms and derivations
Double-cyclic codes
Gray map
Skew-cyclic codes
ISSN: 19305346
Author Scopus IDs: 55605770443
Author Affiliations: Sharma, A., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Bhaintwal, M., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Funding Details: This work was partially supported by DST, Govt. of India, under Grant No. SB/S4/MS: 893/14. Also, the first author would like to thank the Council of Scientific & Industrial Research (CSIR), India for providing financial support. The authors would also like to thank the anonymous referees for their valuable comments and suggestions.
Corresponding Author: Sharma, A.; Department of Mathematics, Indian Institute of Technology RoorkeeIndia; email:
Appears in Collections:Journal Publications [MA]

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