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One generator quasi-cyclic codes over F2 + uF2 + vF2 + uvF2 [article]

Srinivasulu B, Maheshanand Bhaintwal
2017 arXiv   pre-print
In this paper, we study the structure of 1-generator quasi-cyclic codes over the ring R = F2 + uF2 + vF2 + uvF2, with u2 = v2 = 0 and uv = vu. We determine the minimal spanning sets for these codes.  ...  As a generalization of these codes, we also investigate the structure of 1-generator generalized quasi-cyclic codes over R and determine a BCH type bound for them.  ...  Structure of 1-generator quasi-cyclic codes over R Let l be a positive integer.  ... 
arXiv:1602.00139v3 fatcat:babccwoubrea3aoiwtt4cvmswq

Cyclic DNA codes over F2+uF2+vF2+uvF2 [article]

Shixin Zhu, Xiaojing Chen
2015 arXiv   pre-print
In this work, we study the structure of cyclic DNA codes of arbitrary lengths over the ring R=F2+uF2+vF2+uvF2 and establish relations to codes over R1=F2+uF2 by defining a Gray map between R and R1^2 where  ...  Cyclic codes of arbitrary lengths over R satisfied the reverse constraint and the reverse-complement constraint are studied in this paper. The GC content constraint is considered in the last.  ...  We will give one of the main conclutions below. Theorem 3.8 Let C = vC 1 ⊕ (1 + v)C 2 be a cyclic code of arbitrary lengths n over R.  ... 
arXiv:1508.07113v1 fatcat:e4nezvj4avfmzamnn36f34hjoa

The structure of duals of cyclic codes over 𝔽2 + u𝔽2 + v𝔽2 + uv𝔽2 and some DNA codes

Srinivasulu Bathala, Maheshanand Bhaintwal
2017 International Journal of Information and Coding Theory  
In this paper, we study the structure of duals of cyclic codes over the ring R = F2 + uF2 + vF2 + uvF2, u 2 = v 2 = 0, uv = vu. We determine a unique set of generators for these codes.  ...  Reference to this paper should be made as follows: Srinivasulu, B. and Bhaintwal, M. (2017) 'The structure of duals of cyclic codes over F2 + uF2 + vF2 + uvF2 and some DNA codes', Int. studied codes over  ...  length n are quasi-cyclic codes of index six and of length 6n over the alphabet {A, G, C, T }.  ... 
doi:10.1504/ijicot.2017.081463 fatcat:rnz4u3di4zbyfm7atxvtn3hdta