Let k be a non-zero complex number. In this paper, we consider a k -circulant matrix whose first row is (Mₛ, Mₒ+ₓ, Mₒ+₂ₓ, , Mₒ+ (₍-₂) ₓ, Mₒ+ (₍-₁) ₓ), where Mₛ is the n^th Mersenne number, s is a non-negative integer and t is a positive integer. The formulae for the eigenvalues of such matrix are obtained. That formulae improve the result of Theorem 2. 3. 20 (because the result of Theorem 2. 3. 20 can not be applied in some cases) and show that there are cases when the result of Theorem 2. 9. 20 can also not be applied. Then, we consider the norms of such matrix. Namely, the obtained formulae for the 1-norm, the -norm, the Euclidean norm and the spectral norm of such matrix extend (and correct) the results of, respectively, Theorem 3. 3. 20, Theorem 3. 4. 20 and Theorem 3. 6. 20. At the end of the paper, we also obtain the bounds for the spectral norm of a k -circulant matrix whose first row is (Mₛ^-1, Mₒ+ₓ^-1, Mₒ+₂ₓ^-1, , Mₒ+ (₍-₂) ₓ^-1, Mₒ+ (₍-₁) ₓ^-1) provided that s is a positive integer.
Biljana Radičić (Wed,) studied this question.