Small-weight codewords of algebraic geometry codes
Alberto Ravagnani · Bollettino Della Unione Matematica Italiana · 2025
Abstract We present a general method for characterizing the supports of small-weight codewords of algebraic geometry codes. We apply the method to investigate the weight distributions of error-correcting codes constructed from the Hermitian curve and from norm-trace curves, providing closed formulas for several parameter sets. The results presented in this paper draw on E. Ballico’s contributions to the connection between coding theory and algebraic geometry.