Title :
Generalized Hamming weights of q-ary Reed-Muller codes
Author :
Heijnen, Petra ; Pellikaan, Ruud
Author_Institution :
Dept. of Math. & Comput. Sci., Eindhoven Univ. of Technol., Netherlands
fDate :
1/1/1998 12:00:00 AM
Abstract :
The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as well as the q-ary Reed-Muller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain condition
Keywords :
Goppa codes; Hamming codes; Reed-Muller codes; algebraic geometric codes; algebraic geometry codes; double chain condition; generalized Hamming weights; one point geometric Goppa codes; order bound; order functions; q-ary Reed-Muller codes; Galois fields; Hamming weight; Linear code; Mathematics; Polynomials; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
