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Paper   IPM / M / 151
School of Mathematics
  Title:   Ternary trades and their codes
1.  G. B. Khosrovshahi
2.  R. Naserasr
3.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: J. Statist. Plann. Inference
  Vol.:  95
  Year:  2001
  Pages:   237-243
  Supported by:  IPM
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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