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RunLength Constraint of Cyclic ReverseComplement and Constant GCContent DNA Codes
Ramy TAKI ELDIN Hajime MATSUI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E103A
No.1
pp.325333 Publication Date: 2020/01/01
Online ISSN: 17451337
DOI: 10.1587/transfun.2019EAP1053
Type of Manuscript: PAPER Category: Coding Theory Keyword: Finite fields, irreducible cyclic codes, weight distribution, trace function, ranknullity theorem,
Full Text: PDF(773.6KB)>>
Summary:
In DNA data storage and computation, DNA strands are required to meet certain combinatorial constraints. This paper shows how some of these constraints can be achieved simultaneously. First, we use the algebraic structure of irreducible cyclic codes over finite fields to generate cyclic DNA codes that satisfy reverse and complement properties. We show how such DNA codes can meet constant guaninecytosine content constraint by MacWilliamsSeery algorithm. Second, we consider fulfilling the runlength constraint in parallel with the above constraints, which allows a maximum predetermined number of consecutive duplicates of the same symbol in each DNA strand. Since irreducible cyclic codes can be represented in terms of the trace function over finite field extensions, the linearity of the trace function is used to fulfill a predefined runlength constraint. Thus, we provide an algorithm for constructing cyclic DNA codes with the above properties including runlength constraint. We show numerical examples to demonstrate our algorithms generating such a set of DNA strands with all the prescribed constraints.

