Generators of negacyclic codes over Fp[u, v]/⟨u2, v2, uv, vu⟩ of length ps

We consider a local non-Frobenius ring Rp = F-p[u, v]/< u(2), v(2), uv, vu > defined for each prime number p and study the ideal representation of the ring R-p[x]/< x(n) + 1 >, which is well-known to be related to negacyclic codes over R-p of length n = p(s) with s >= 1. We assume that n is a power of p, and under this setting, we show that a specific class of ideals can be represented uniquely in terms of degrees related to its generators. We also give a lower bound of the minimum Hamming distances of negacyclic codes over R-p, and show that the lower bound is sharp for several codes whose corresponding ideals of R-p[x]/< x(n) + 1 > belong to the aforementioned class.