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On the norm and covering radius of the first-order Reed-Muller codes

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1 Author(s)
Xiang-dong Hou ; Dept. of Math. & Stat., Wright State Univ., Dayton, OH, USA

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

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Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 3 )