Ternary trades and their codes
نویسنده
چکیده
In this paper, the notion of trades over finite fields is introduced. In particular, trades over GF (3) (ternary trades) are studied. By considering the incidence matrix of t-subsets vs. k-subsets of a v-set as a parity check matrix of a ternary code, we obtain a new family of codes in which every codeword is a ternary trade. The spectrum of weights of these codes is discussed; a simple and fast algorithm for decoding is given; and the automorphism group of the codes is determined. We also provide a table of all non-isomorphic ternary trades of weight at most 12. AMS classification: 05B05; 94B05; 94B35
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