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The t-wise intersection of relative three-weight codes

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The $t$-wise intersection is a useful property of a linear code due to its many applications. Recently, the second author determined the $t$-wise intersection of a relative two-weight code. By using this result and generalizing the finite projective geometry method, we will present the $t$-wise intersection of a relative three-weight code and its applications in this paper.

Abstract

The $t$-wise intersection is a useful property of a linear code due to its many applications. Recently, the second author determined the $t$-wise intersection of a relative two-weight code. By using this result and generalizing the finite projective geometry method, we will present the $t$-wise intersection of a relative three-weight code and its applications in this paper.

참고문헌 (10)

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  2. W. D. Chen, "The weight hierarchies of q-ary codes of dimension 4", IEEE Trans. Inform. Theory, 42(6), pp.2265~2272 (1996)
  3. G. Cohen, "Intersecting codes and separating codes", Discrete Appl. Math, 128(1), pp.75~83 (2003)
  4. G. Cohen, "Linear intersecting codes", Discrete Math, 56(1), pp.35~43 (1985)
  5. G. Cohen, "Upper bounds on separating codes", IEEE Trans. Inform. Theory, 50(6), pp.1291~1295 (2004)
  6. G. Cohen, "Intersecting codes and independent families", IEEE Trans. Inform. Theory, 40, pp.1872~1881 (1994)
  7. S. Encheva, "Constructions of intersecting codes", IEEE Trans. Inform. Theory, 45(4), pp.1234~1237 (1999)
  8. Z. H. Liu, "The t-wise intersection of relative two weight codes", Sci. China Math, 57(8), pp.1765~1770 (2014)
  9. Z. H. Liu, "On relative constant-weight codes", Des. Codes Cryptogr, 75(1), pp.127~144 (2015)
  10. G. B. Rassard, "Information-theoretic reductions among disclosure problems", Proc. 27th IEEE Symp. Foundat. Comput. Sci, pp.168~173 (1986)

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