On optimal linear codes over

Let n q ( k , d ) be the smallest integer n for which there exists a linear code of length n , dimension k and minimum distance d over F q , the field of q elements. We determine n 5 ( 5 , d ) for d = 476 – 479 , 491–530, 538–540, 542–560, 563–625. We also show that n 5 ( 5 , d ) ≥ g 5 ( 5 , d ) + 1 for d = 70 – 120 , 144–150, 268–275, 280–290, 293–300, 394, 395, 398–400 and that n 5 ( 5 , d ) ≥ g 5 ( 5 , d ) + 2 for d = 373 – 375 and so on, where g q ( k , d ) = ∑ i = 0 k − 1 ⌈ d / q i ⌉ .