Characterization results on arbitrary non-weighted minihypers and on linear codes meeting the Griesmer bound
نویسندگان
چکیده
We present characterization results on non-weighted minihypers. For minihypers in PG(k − 1, q), q not a square, we improve greatly the results of Hamada, Helleseth, and Maekawa, and of Ferret and Storme. The largest improvements are obtained for q prime.
منابع مشابه
Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound
We present characterization results on weighted minihypers. We prove the weighted version of the original results of Hamada, Helleseth, and Maekawa. Following from the equivalence between minihypers and linear codes meeting the Griesmer bound, these characterization results are equivalent to characterization results on linear codes meeting the Griesmer bound. 1. Linear codes meeting the Griesme...
متن کاملOn weighted { δv μ + 1 , δv μ ; k − 1 , q } - minihypers , q square
Weighted minihypers have recently received a lot of attention. They originated as geometrical equivalents of linear codes meeting the Griesmer bound, but have also been investigated for their importance in solving geometrical problems. Storme characterized weighted {δ(q+1), δ; k−1, q}-minihypers, q square, as a sum of lines and Baer subgeometries PG(3, √ q), provided δ is sufficiently small. Th...
متن کاملLinear codes meeting the Griesmer bound, minihypers, and geometric applications
Coding theory and Galois geometries are two research areas which greatly influence each other. In this talk, we focus on the link between linear codes meeting the Griesmer bound and minihypers in finite projective spaces. Minihypers are particular (multiple) blocking sets. We present characterization results on minihypers, leading to equivalent characterization results on linear codes meeting t...
متن کاملTight sets, weighted m -covers, weighted m -ovoids, and minihypers
Minihypers are substructures of projective spaces introduced to study linear codes meeting the Griesmer bound. Recently, many results in finite geometry were obtained by applying characterization results on minihypers [8, 17, 18]. In this paper, using characterization results on certain minihypers, we present new results on tight sets in classical finite polar spaces and weighted m-covers, and ...
متن کاملNew classification results for a certain class of weighted minihypers
Minihypers were introduced for their relation with linear codes meeting the Griesmer bound. Results on minihypers have therefore important applications in coding theory. On the other hand, minihypers are nice geometrical structures since they are a generalization of blocking sets, which have been studied a lot. Therefore also minihypers deserve to be studied from a purely geometrical point of v...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Des. Codes Cryptography
دوره 49 شماره
صفحات -
تاریخ انتشار 2008