A characterization of some {3v(1)+v(3),3v(0)+v(2);3,3}-minihypers and its applications to error-correcting codes

Recently, Hamada et al. (Des. Codes Cryptogr. 2(1992), 225-229) showed that there exists an [87,5,57;3]-code meeting the Grismer bound. But it is unknown whether or not an [87,5,57;3]-code is unique up to equivalence. in order to characterize all [87,5,57;3]-codes, it is sufficient to characterize all {2v(2) + 2v(3), 2v(1) + 2v(2); 4,3}-minihypers and in order to characterize all {2v(2) + 2v(3), 2v(1) + 2v(2); 4,3}-minihypers, it is necessary to characterize all {3v(1) + v(3), 3v(0) + v(2); 3,3}-minihypers, where v(0) = 0, v(1) = 1, v(2) = 4 and v(3) = 13 (cf. Hamada and Helleseth, J. Statist. Plann. Inference, 56 (1996)). The purpose of this paper is to characterize all {3v(1) + v(3), 3v(0) + v(2); 3, 3}-minihypers.