Several classes of BCH codes of length n=qᵐ-12

BCH codes are an important class of cyclic codes, and have wide applications in communication and storage systems. In this paper, we study the negacyclic BCH code and cyclic BCH code of length n=qᵐ-1/2.For negacyclic BCH code, we give the dimensions of C(n,-1,δ,0) for δ =aqᵐ-1/q-1,aqᵐ⁻¹-1(1≤ a <q-1/2) and δ =aqᵐ-1/q-1+bqᵐ-1/q²-1,aqᵐ⁻¹+(a+b)qᵐ⁻²-1 (2 m,1≤ a+b ≤ q-1,q-a-2/2≥ 1). The dimensions of negacyclic BCH codes C(n,-1,δ,0) with few nonzeros and C(n,-1,δ,b) with b≠ 1 are settled.For cyclic BCH code, we give the weight distributions of extended codes C̄(n,1,δ,1) for δ=δ₁,δ₂ and the parameters of dual code C⊥(n,1,δ,1) for δ₂≤ δ ≤ δ₁.