Run-Length Constraint of Cyclic Reverse-Complement and Constant GC-Content DNA Codes

Ramy TAKI ELDIN  Hajime MATSUI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.1   pp.325-333
Publication Date: 2020/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1053
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
Finite fields,  irreducible cyclic codes,  weight distribution,  trace function,  rank-nullity theorem,  

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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 guanine-cytosine content constraint by MacWilliams-Seery algorithm. Second, we consider fulfilling the run-length 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 run-length constraint. Thus, we provide an algorithm for constructing cyclic DNA codes with the above properties including run-length constraint. We show numerical examples to demonstrate our algorithms generating such a set of DNA strands with all the prescribed constraints.