Title :
On the norm and covering radius of the first-order Reed-Muller codes
Author_Institution :
Dept. of Math. & Stat., Wright State Univ., Dayton, OH, USA
fDate :
5/1/1997 12:00:00 AM
Abstract :
Let ρ(1,m) and N(1,m) be the covering radius and norm of the first-order Reed-Muller code R(1,m), respectively. It is known that ρ(1,2k+1)⩽lower bound [22k-2(2k-1/2)] and N(1,2k+1)⩽2 lower bound [22k-2(2k-1/2)] (k>0). We prove that ρ(1,2k+1)⩽2 lower bound [22k-1-2(2k-3/2)] and N(1,2k+1)⩽4 lower bound [22k-1-2(2k-3/2)] (k>0). We also discuss the connections of the two new bounds with other coding theoretic problems
Keywords :
Reed-Muller codes; linear codes; binary linear code; coding theoretic problems; covering radius; first-order Reed-Muller codes; norm; upper bound; Error correction codes; Hamming distance; Linear code; Mathematics; Statistics; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on