Single Edit Error-Correcting DNA Codes with Multiple Biological and Combinatorial Constraints: An Algebraic Approach

Inspired by G. Tenengolts' 1984 construction of nonbinary single error-correcting codes for deletion and insertion errors, we develop families of DNA codes that simultaneously address multiple biological and combinatorial constraints. These codes satisfy Hamming, Reverse, Reverse-Complement, and GCcontent constraints while maintaining single error-correction capabilities for insertion, deletion, and substitution errors. Additionally, our constructed codes are free from homopolymers exceeding run length four and from secondary structures with stem lengths greater than two, both in individual codewords and their concatenations. This work presents the first known construction of DNA codes capable of single-error correction (insertion, deletion, and substitution) while satisfying multiple constraints: the GC-content constraint, Hamming constraint, Reverse constraint, and Reverse-Complement constraint. Additionally, these codes are constructed to be free from homopolymers exceeding run length four and secondary structures with stem lengths greater than two.