A characterization of some {3vμ + 1, 3vμ; k - 1, q}-minihypers and some [n, k, qk-1 - 3qμ; q]-codes (k ⩾ 3, q ⩾ 5, 1 ⩽ μ < k - 1) meeting the Griesmer bound

✍ Scribed by Noboru Hamada; Tor Helleseth

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 433 KB
• Volume: 146
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)00157-3

✦ Synopsis

For any In, k, d; q]-code the Griesmer bound says that n >t ~ F d/q' 7. The purpose of this paper is to characterize all In, k, qk-1 _ 3q~; q]-codes meeting the Griesmer bound in the case where k >/3, q >~ 5 and 1 ~</~ < k -1. It is shown that all such codes have a generator matrix whose columns correspond to all points in PG(k -1, q) except for the points in a disjoint union of three p-flats in PG(k -l, q).