Formal duality of linearly presentable codes over a Galois field

  • Alexander A. Nechaev
  • Alexey S. Kuzmin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1255)


In [4] it was shown, that the weight enumerators of two binary ℤ4-linearly dual codes satisfy the McWilliams identity (i.e. these codes are formally dual). If we consider an arbitrary Galois ring R=GR(q2, p2) of characteristic p2 and a pair of R-linearly dual codes over a Galois field GF(q) this result is not preserved. We propose the approach to correcting this disadvantage. The titled codes are presented as codes inthe alphabet =RS q (q,2), being a Reed-Solomon code. The appropriate exact weight enumerators of these codes are reduced to some projective weight enumerators (obtained by identifying of variables) which satisfy the McWilliams identity for linear codes over GF(q). We discuss ways of “optimal” identifying of variables such that the corresponding projective weight enumerators allow us to construct complete weight enumerators of the initial codes over GF(q).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Alexander A. Nechaev
    • 1
  • Alexey S. Kuzmin
    • 1
  1. 1.Center of New Informational TechnologiesMoscow State UniversityRussia

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