New minimum distance bounds for certain binary linear codes

Let an n, k, d]-code denote a binary linear code of length n, dimension k, and minimum distance at least d. Define d(n, k) as the maximum value of d for which there exists a binary linear n, k, d]-code. T. Verhoeff (1989) has provided an updated table of bounds on d(n, k) for 1⩽k⩽n⩽127. The authors improve on some of the upper bounds given in that table by proving the nonexistence of codes with certain parameters