Derived Forms and Binary Linear Codes
نویسنده
چکیده
Derived forms defined by M. Aschbacher in [1] are closely related to combinatorial polarization introduced by H. N. Ward in [6]. A binary linear code is said to be of (divisibility) level r, if r is the biggest integer such that 2r divides the weight of each codeword. In this paper, we study the relation between functions of combinatorial degreee r+1 and binary linear codes of level r. We associate a code of level at least r with every function of combinatorial degree r + 1 (as a generalization of the case r = 2 considered by O. Chein and E. Goodaire), and vice versa. Several examples are provided.
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