New construction of codes from algebraic curves

Abstract

A new construction of linear codes from algebraic curves is introduced. In essence, the construction is of the BCH type, namely, it is to extend the method of constructing BCH codes to the construction of codes from algebraic curves. As a consequence, a new class of codes is constructed without relying much on algebraic geometry. A comparison to algebraic-geometric codes from Hermitian curves showed that our codes typically have much larger minimum distance at a higher code rate. In particular, compared to Hermitian codes on H(2/sup /spl alpha//), which have length 2/sup 3/spl alpha//, then, at a higher code rate, our codes have a minimum distance of at least 2/sup [/spl alpha//4]/ times greater than that of the Hermitian codes. Examples have also shown that, for the same code length and designed minimum distance, our codes can have higher dimension compared to codes constructed from the approach given by Feng and Rao (see IEEE Trans. Inform. Theory, vol.40, pp.981-1002, July 1994).