Title :
An Elementary Approach to Ax-Katz, McEliece´s Divisibility and Applications to Quasi-Perfect Binary 2-Error Correcting Codes
Author :
Castro, F.N. ; Rubio, Isabel ; Randriam, Hugues
Author_Institution :
Dept. of Math., Puerto Rico Univ., Rio Piedras
Abstract :
In this paper we present an algorithmic approach to the problem of the divisibility of the number of solutions to a system of polynomial equations. Using this method we prove that all binary cyclic codes with two zeros over F2f and minimum distance 5 are quasi-perfect for f les 10. We also present elementary proofs of divisibility results that, in some cases, improve previous results
Keywords :
binary codes; error correction codes; polynomials; algorithmic approach; binary cyclic codes; error correcting codes; polynomial equations; quasi-perfect binary codes; Computer science; Cryptography; Equations; Error correction codes; Galois fields; Integer linear programming; Mathematics; Polynomials;
Conference_Titel :
Information Theory, 2006 IEEE International Symposium on
Conference_Location :
Seattle, WA
Print_ISBN :
1-4244-0505-X
Electronic_ISBN :
1-4244-0504-1
DOI :
10.1109/ISIT.2006.261812
