Abstract
In this paper the weight distribution of binary Goppa codes with location set GF (2m) and irreducible quadratic Goppa polynomial is studied. These codes are all equivalent and have parameters [2m, 2m–2m, 5]. An explicit formula for the number of codewords of weight 5 and 6 is derived. The weight distribution of the dual codes is related to the weight distribution of a reversible irreducible cyclic code of length 2m+1 and dimension 2m whose weights can be expressed in terms of Kloosterman sums over GF (2m). As numerical examples the weight distribution of the double-error-correcting Goppa codes of block length 8,16,32, and 64 are computed.
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Dür, A. (1988). The weight distribution of double-error-correcting goppa codes. In: Beth, T., Clausen, M. (eds) Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra. AAECC 1986. Lecture Notes in Computer Science, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039177
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DOI: https://doi.org/10.1007/BFb0039177
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