Construction Techniques of Generator Polynomials of BCH Codes

LetA0⊂A1⊂···⊂At−1⊂Atbe a chain of unitary commutative rings (eachAiis constructed bythe direct product of suitable Galois rings with multiplicative groupA∗iof units) andK0⊂K1⊂···⊂Kt−1⊂Ktbe the corresponding chain of unitary commutative rings (eachKiis constructed by thedirect product of corresponding residue fields of given Galois rings, with multiplicative groupsK∗iofunits), wheretis a non negative integer. In this work presents three different types of constructionsof generator polynomials of sequences of BCH codes having entries fromA∗iandK∗ifor eachi,where0≤i≤t