Golomb and Gong (1997 and 1999) considered binary sequences with the trinomial property. In this correspondence we shall show that the sets of those sequences are (quite trivially) closely connected with binary cyclic codes with codewords of weight three. This approach gives us another way to deal with trinomial property problems. After disproving one conjecture formulated by Golomb and Gong, we exhibit an infinite class of sequences which do not have the trinomial property, corresponding to binary cyclic codes of length 2/sup m/-1 with minimum distance exactly four.

P. Deligne's theorem (1974) is used to prove that the covering radius of a primitive binary BCH code with designed distance 2t+1 is equal to 2t-1 if t is of the form 2/sup u/+1 and the code length is at least (2t)/sup 4t-2/. It is believed that this is the first time Deligne's theorem is used on coding theory.>

P. Delsarte (1973) developed a method that gives an upper bound on the cardinality of a code as a function of its minimum distance. It is shown that, using a modification of that method, one gets an upper bound on the covering radius of a code as a function of its dual distance. As an interesting special case, the covering radius of the dual of a BCH code is considered.>