Additive cyclic codes over mixed alphabets and the football pool problem

Motivated by a generalization of the football pool problem, we introduce additive cyclic codes over mixed alphabets of the form 𝔽q1 × 𝔽q2 where q1 = p1m1, q2 = p2m2 for distinct primes p1,p2. We study their algebraic properties, generating sets, and duals. Additionally, we give examples of additive cyclic codes over the alphabet ℤ2ℤ3 that have best-known or optimal parameters.