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    Generalizing binary quadratic residue codes to higher power residues over larger fields

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    chartersp89962.pdf (322.2Kb)
    Date
    2009-05
    Author
    Charters, Philippa Liana
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    Abstract
    In this paper, we provide a generalization of binary quadratic residue codes to the cases of higher power prime residues over the finite field of the same order, which we will call qth power residue codes. We find generating polynomials for such codes, define a new notion corresponding to the binary concept of an idempotent, and use this to find square root lower bound for the codeword weight of the duals of such codes, which leads to a lower bound on the weight of the codewords themselves. In addition, we construct a family of asymptotically bad qth power residue codes.
    Department
    Mathematics
    Description
    text
    Subject
    Binary quadratic residue codes
    Higher power prime residues
    Finite field
    Residue codes
    Idempotent
    URI
    http://hdl.handle.net/2152/11667
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