Skew Cyclic Codes over a Non-chain Ring

2017 ◽  
Vol 26 (3) ◽  
pp. 544-547 ◽  
Author(s):  
Minjia Shi ◽  
Ting Yao ◽  
Patrick Solé
Keyword(s):  
Cyclic Codes ◽  
Chain Ring ◽  
Skew Cyclic Codes

scholarly journals Hartmann–Tzeng bound and skew cyclic codes of designed Hamming distance

2018 ◽  
Vol 50 ◽  
pp. 84-112 ◽  
Author(s):  
José Gómez-Torrecillas ◽  
F.J. Lobillo ◽  
Gabriel Navarro ◽  
Alessando Neri
Keyword(s):  
Hamming Distance ◽  
Cyclic Codes ◽  
Skew Cyclic Codes

A Note on Skew Cyclic Codes over a Class of Rings

2020 ◽  
Vol 27 (04) ◽  
pp. 703-712
Author(s):  
Hai Q. Dinh ◽  
Bac T. Nguyen ◽  
Songsak Sriboonchitta
Keyword(s):  
Finite Field ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
General Setting ◽  
Constacyclic Codes ◽  
Arbitrary Length ◽  
Skew Cyclic Codes

We study skew cyclic codes over a class of rings [Formula: see text], where each [Formula: see text] [Formula: see text] is a finite field. We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R. Moreover, we discuss possible extension of our results in the more general setting of [Formula: see text]-dual skew constacyclic codes over R, where δR is an automorphism of R.

scholarly journals Skew cyclic codes over 𝔽4R

2020 ◽  
pp. 2250065
Author(s):  
Nasreddine Benbelkacem ◽  
Martianus Frederic Ezerman ◽  
Taher Abualrub ◽  
Nuh Aydin ◽  
Aicha Batoul
Keyword(s):  
Error Control ◽  
Cyclic Codes ◽  
Gray Map ◽  
Inner Product ◽  
Algebraic Structures ◽  
Error Control Codes ◽  
Dna Codes ◽  
Natural Connection ◽  
Skew Cyclic Codes

This paper considers a new alphabet set, which is a ring that we call [Formula: see text], to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize [Formula: see text]-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over [Formula: see text] are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of [Formula: see text]-skew cyclic codes which are reversible complement.

Skew cyclic codes over 𝔽p + u𝔽p

2018 ◽  
Vol 5 (1) ◽  
pp. 81
Author(s):  
R. Dastbasteh ◽  
H. Mousavi ◽  
T. Abualrub ◽  
N. Aydin ◽  
J. Haghighat
Keyword(s):  
Cyclic Codes ◽  
Skew Cyclic Codes
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