The algebraic decoding of Goppa codes

An interesting class of linear error-correcting codes has been found by Goppa [3], [4]. This paper presents algebraic decoding algorithms for the Goppa codes. These algorithms are only a little more complex than Berlekamp's well-known algorithm for BCH codes and, in fact, make essential use of his procedure. Hence the cost of decoding a Goppa code is similar to the cost of decoding a BCH code of comparable block length.

[1]  Masao Kasahara,et al.  A Method for Solving Key Equation for Decoding Goppa Codes , 1975, Inf. Control..

[2]  Elwyn R. Berlekamp,et al.  Goppa Codes , 2022 .

[3]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[4]  Jacobus H. van Lint,et al.  Coding Theory , 1971 .