Isometric embeddings of Z(p)k in the hamming space F-p(N) and Z(p)k-linear codes
Isometric embeddings of Z(pn+1) into the Hamming space (F-p(pn), w) have played a fundamental role in recent constructions of non-linear codes. The codes thus obtained are very good codes, but their rate is limited by the rate of the first-order generalized Reed-Muller code-hence, when n is not very small, these embeddings lead to the construction of low-rate codes. A natural question is whether there are embeddings with higher rates than the known ones. In this paper, we provide a partial answer to this question by establishing a lower bound on the order of a symmetry of (F-p(N), w).
isometric embedding codes over rings symmetry group reed-muller code