FINITE QUASI-FROBENIUS MODULES AND LINEAR CODES

@article{Greferath2004FINITEQM,
  title={FINITE QUASI-FROBENIUS MODULES AND LINEAR CODES},
  author={M. Greferath and A. Nechaev and R. Wisbauer},
  journal={Journal of Algebra and Its Applications},
  year={2004},
  volume={03},
  pages={247-272}
}
  • M. Greferath, A. Nechaev, R. Wisbauer
  • Published 2004
  • Mathematics
  • Journal of Algebra and Its Applications
  • The theory of linear codes over finite fields has been extended by A. Nechaev to codes over quasi-Frobenius modules over commutative rings, and by J. Wood to codes over (not necessarily commutative) finite Frobenius rings. In the present paper, we subsume these results by studying linear codes over quasi-Frobenius and Frobenius modules over any finite ring. Using the character module of the ring as alphabet, we show that fundamental results like MacWilliams' theorems on weight enumerators and… CONTINUE READING
    59 Citations
    Self-dual codes over commutative Frobenius rings
    • 91
    • PDF
    On the equivalence of codes over rings and modules
    • 35
    Some remarks on non projective Frobenius algebras and linear codes
    • 1
    • PDF
    On the weight distribution of codes over finite rings
    • E. Byrne
    • Mathematics, Computer Science
    • Adv. Math. Commun.
    • 2011
    • 5
    • PDF
    Gröbner Bases over Commutative Rings and Applications to Coding Theory
    • E. Byrne, T. Mora
    • Mathematics, Computer Science
    • Gröbner Bases, Coding, and Cryptography
    • 2009
    • 12
    Extension Theorems for Various Weight Functions over Frobenius Bimodules
    • 2
    • PDF
    Parity check systems of nonlinear codes over finite commutative Frobenius rings
    • 1
    • Highly Influenced
    • PDF
    Finite Rings with Applications
    • 37

    References

    SHOWING 1-10 OF 45 REFERENCES
    Duality for modules over finite rings and applications to coding theory
    • 319
    • Highly Influential
    • PDF
    Extension Theorems for Linear Codes over Finite Rings
    • J. Wood
    • Mathematics, Computer Science
    • AAECC
    • 1997
    • 42
    • PDF
    Finite-Ring Combinatorics and MacWilliams' Equivalence Theorem
    • 121
    • PDF
    Characterization of finite Frobenius rings
    • 94
    Characters and the Equivalence of Codes
    • H. Ward, J. Wood
    • Mathematics, Computer Science
    • J. Comb. Theory, Ser. A
    • 1996
    • 54
    A field-like property of finite rings
    • 29
    The Theory of Error-Correcting Codes
    • 7,211
    • PDF