On equivalence of cyclic and dihedral zero-divisor codes having nilpotents of nilpotency degree two as generators

Abstract Zero-divisor codes are constructed using group rings where their generators zero-divisors. Generally, zero-divisor can be equivalent despite associated groups non-isomorphic, leading to the proposed conjecture “Every dihedral code has an form of cyclic code”. This paper is devoted study equivalence in $$F_2G$$ F 2 G having from 2-nilradical , consisting all nilpotents nilpotency degree 2 . Essentially, algebraic structures 2-nilradicals first studied general for both commutative and non-commutative before specialized into case when G dihedral. Then, results used above cases respective 2-nilradicals.