AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Extended norm-trace codes with optimized correction capability
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On codes from norm-trace curves
Finite Fields and Their Applications
A new method for constructing small-bias spaces from hermitian codes
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
On the subfield subcodes of Hermitian codes
Designs, Codes and Cryptography
| Hi-index | 754.84 |
In two previous papers, the first by Feng, Rao, Berg, and Zhu (see ibid., vol.43, p.1799-810, 1997) and the second by Feng, Zhu, Shi, and Rao (see Proc. 35th. Afferton Conf. Communication, Control and Computing, p.205-14, 1997), the authors use a generalization of Bezout's theorem to estimate the minimum distance and generalized Hamming weights for a class of error correcting codes obtained by evaluation of polynomials in points of an algebraic curve. The main aim of this article is to show that instead of using this rather complex method the same results and some improvements can be obtained by using the so-called footprint from Grobner basis theory. We also develop the theory further such that the minimum distance and the generalized Hamming weights not only can be estimated but also can actually be determined