The weight distributions of cosets are not known for the class of binary 2-error-correcting BCH codes of length n=2/sup m/-1, m even (the nonuniformly packed case). By using the graph theoretical concepts of the combinatorial matrix of a code and an r-partition design introduced in previous works, the authors obtain these distributions of cosets in the three particular cases of length 15, 63, and 255. It is observed that in these three cases the number of distinct weight distributions is a constant equal to 8.>

In this correspondence, we apply a theorem in finite geometry to obtain an improvement of the codes recently introduced by Séguin, Allard, and Bhargava to provide error protection for data in the ASCII format. Our construction yields a fast decoding algorithm.

Using the Fourier transform for vector spaces over the finite field GF(p^{m}), a characterization ofN-weight linear codes is given. Some particular cases containing Camion's relations for two parameters' difference sets are examined, and a construction using the notion of normal spread is given.