@techreport{oai:kanazawa-u.repo.nii.ac.jp:00011971,
 month = {May},
 note = {BCH codes are subclass of cyclic codes with strong properties and have been known for years. In 1994, Chen, Reed, Helleseth, and Truong proposed a decoding procedure for t-error-correcting codes via CRHT syndrome variety using computation of lexicographical Gr¨obner bases of the ideal. In 2005, Orsini and Sala added polynomial χl,l˜, 1 ≤ l < l˜≤ t, to a system of algebraic equations I to make sure that the position of any two errors are distinct or at least one of them is zero. In 2014, Takuya Fushisato proposed a modified system J to solve 2-error-correcting BCH codes problem. Here the polynomial τj ∈ J is a divisor of σj and contain all possible syndromes of type 0, αi1 , αi1 + αi2 ∈ Fqm as roots. Generally, τj may be regarded as the minimal polynomial of the roots. In this paper, Fushisato’s system is generalized into K in which Ωj ∈ K contains all possible roots of t-error-correcting BCH codes in the set Sol ⊆ Fqm . Using the system of polyno-mials K, the general error locator polynomials of 3-error-correcting codes could be computed and the computation time of some codes were reduced., Selected Papers from the International Symposium on Computational Science - International Symposium on Computational Science Kanazawa University, Japan},
 title = {Computing general error locator polynomial of 3-error-correcting BCH codes via syndrome varieties using minimal polynomial},
 year = {2015}
}