NEW METRICS ARISING FROM MATROIDS OF LINEAR CODES
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In this paper, from each linear code in Fnq, we construct two metrics, the one called “the metric associated to it” and the other “the symmetrized metric associated to it.” They are respectively defined interms of the rank function and the rank and corank functions of the matroid of the linear code. Such metrics constructed from linear codes give rise to abundant new metrics on the space Fnq. We investigate their properties and illustrate our results with some examples.
Abstract
In this paper, from each linear code in Fnq, we construct two metrics, the one called “the metric associated to it” and the other “the symmetrized metric associated to it.” They are respectively defined interms of the rank function and the rank and corank functions of the matroid of the linear code. Such metrics constructed from linear codes give rise to abundant new metrics on the space Fnq. We investigate their properties and illustrate our results with some examples.
참고문헌 (5)
- T. Britz, "T. Britz, Code enumerators and Tutte polynomials", IEEE Trans. Inform. Theory, 56, pp.4350~4358 (2010)
- J. Y. Hyun, "Maximum distance separable poset codes", Des. Codes Cryptogr., 48, pp.247~261 (2008)
- F. J. MacWilliams, "The Theory of Error Correcting Codes" (1998), North-Holland
- D. S. Kim, "MacWilliams-type identities for fragment and sphere enumerators", Europ. J. Combin., 28, pp.273~302 (2007)
- D. J. A. Welsh, "Matroid Theory" (1976), Academic Press