Cyclic completely regular codes C1,5

We construct a family of cyclic completely regular codes (CRCs) of length n=2ᵐ-1 n = 2 m - 1 and compute their intersection arrays. These codes, denoted C1,5 C 1 , 5 , are generated by the product m₁(x)m₅(x) m 1 ( x ) m 5 ( x ) , where mᵢ(x) m i ( x ) is the minimal polynomial of α ⁱ α i , and α α is a primitive element of the finite field F2ᵐ F 2 m . We consider two main cases: odd m and m ≡ 2 4 m ≡ 2 ( mod 4 ) . For odd m , these codes are known to be completely regular with covering radius ρ =3 ρ = 3 and minimum distance $$d=5$$ d = 5 . We prove that, for any m , the codes C1,3 C 1 , 3 and C1,5 C 1 , 5 are non-equivalent despite sharing the same parameters and intersection array. For m ≡ 2 4 m ≡