On optimal non-projective ternary linear codes

Mito Takenaka, Kei Okamoto, Tatsuya Maruta
2008 Discrete Mathematics  
We prove the existence of a [406, 6, 270] 3 code and the nonexistence of linear codes with parameters [458, 6, 304] 3 , [467, 6, 310] 3 , [471, 6, 313] 3 , [522, 6, 347] 3 . These yield that n 3 (6, d) = g 3 (6, d) for 268 d 270, n 3 (6, d) = g 3 (6, d) + 1 for d ∈ {280 − 282, 304 − 306, 313 − 315, 347, 348}, n 3 (6, d) = g 3 (6, d) or g 3 (6, d) + 1 for 298 d 301 and n 3 (6, d) = g 3 (6, d) + 1 or g 3 (6, d) + 2 for 310 d 312, where n q (k, d) denotes the minimum length n for which an [n, k, d] q code exists and g q (k, d) = k−1 i=0 d/q i .
doi:10.1016/j.disc.2007.07.044 fatcat:idqmdik4ejhvrdfgzw7zwhqspy