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| Paper IPM / M / 151 |
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| Abstract: | |||||||
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In this paper, the notion of trades over finite fields in 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.
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