MacWilliams relations for spherical orbit codes. (Q1432277)

New explicit MacWilliams identities for two kinds of spaces including spherical orbit codes are presented. One of these identities expresses the distance (Hamming distance) enumerator of the \(p\)-valued linear code \(C\) in terms of the half composition spectrum of the Hamming code which is dual to the code \(C\). The author believes that this identity may be of help in solving the well-known problem of representing the complete weight enumerator of a \(p\)-valued linear code in terms of the parameters of the dual code.