The Re-encoding Transform in Algebraic List Decoding of Algebraic Geometric Codes
Yunqi Wan, Jiongyue Xing, Yuliang Huang, Tingyi Wu, Bo Bob Bai, Gong Zhang · 2023
This paper proposes the re-encoding transformed (ReT) based list decoding using the module basis reduction (BR) interpolation for algebraic geometric (AG) codes on Cabcurves. The two ReT approaches are introduced to facilitate the BR interpolation. One is realized by the bivariate Lagrange polynomial. The other is conducted by the ReT of Reed-Solomon (RS) codes based on the mathematical structure of AG codes. The ReT based BR interpolation (ReT-BR) algorithm for decoding the AG codes is further introduced. Finally, complexity of the proposed algorithm is analyzed and validated by the simulation results, demonstrating its complexity advantage over the non-ReT counterpart.