Corrections to “Weight Distribution of Cosets of Small Codes With Good Dual Properties” [Dec 15 6493-6504]
Louay Bazzi · IEEE Transactions on Information Theory · 2017
We provide two corrections to the above-named work which do not affect the validity of any of the the reported results. First, we note that Conjecture 9 on page 6497 is not correct; a counter example follows from Cohen’s theorem[2]which asserts the existence of linear codes with covering radius up to the sphere-covering bound. The second correction is related to the “Proof of Theorem 2 using Theorem 5” on page 6496. In that proof, the$n$-point Discrete Fourier Transform (DFT) should be on$n+1$points. The other steps of the proof hold without modification. We reproduce below the corrected proof with the needed modifications in bold. The issue with the$n$-point DFT is that it makes Identity(1)below incorrect for$b=n$.