2 research outputs found
Infinite families of 2-designs and 3-designs from linear codes
The interplay between coding theory and -designs started many years ago.
While every -design yields a linear code over every finite field, the
largest for which an infinite family of -designs is derived directly
from a linear or nonlinear code is . Sporadic -designs and -designs
were derived from some linear codes of certain parameters. The major objective
of this paper is to construct many infinite families of -designs and
-designs from linear codes. The parameters of some known -designs are
also derived. In addition, many conjectured infinite families of -designs
are also presented
Narrow-Sense BCH Codes over \gf(q) with Length
Cyclic codes over finite fields are widely employed in communication systems,
storage devices and consumer electronics, as they have efficient encoding and
decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in
most cases among the best cyclic codes. A subclass of good BCH codes are the
narrow-sense BCH codes over \gf(q) with length . Little is
known about this class of BCH codes when . The objective of this paper is
to study some of the codes within this class. In particular, the dimension, the
minimum distance, and the weight distribution of some ternary BCH codes with
length are determined in this paper. A class of ternary BCH codes
meeting the Griesmer bound is identified. An application of some of the BCH
codes in secret sharing is also investigated