An efficient construction of extended length Goppa codes is presented. The construction yields four new binary codes [153, 71, 25], [151, 70, 25], [160, 70, 27], and [158, 69, 27]. The minimum distances are larger than those of the best previously known linear codes of the same length and dimension.
Goppa codes BCH codes
Mathematics Subject Classification
This is a preview of subscription content, log in to check access.
Grassl M.: Bounds on the minimum distance of linear codes and quantum codes. Online available at http://www.codetables.de. Accessed on 21/12/2010 (2007).
MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North Holland, Amsterdam (1983)Google Scholar
Sugiyama Y., Kasahara M., Hirasawa S., Namekawa T.: Further results on Goppa codes and their applications to constructing efficient binary codes. IEEE Trans. Inf. Theory 22(5) 518–526 (1976)CrossRefzbMATHMathSciNetGoogle Scholar