3 research outputs found
Nonexistence of certain singly even self-dual codes with minimal shadow
It is known that there is no extremal singly even self-dual code
with minimal shadow for , , ,
and . In this paper, we study singly even
self-dual codes with minimal shadow having minimum weight for these
. For , and , we show that the weight
enumerator of a singly even self-dual code with minimal shadow
is uniquely determined and we also show that there is no singly even self-dual
code with minimal shadow for , and , respectively. We demonstrate that the weight enumerator of a singly even
self-dual code with minimal shadow is not uniquely determined for parameters
and .Comment: 16 page
Singly even self-dual codes of length and minimum weight
Currently, the existence of an extremal singly even self-dual code of length
is unknown for all nonnegative integers . In this note, we study
singly even self-dual codes. We give some restrictions on
the possible weight enumerators of singly even self-dual
codes with shadows of minimum weight at least for . We discuss a
method for constructing singly even self-dual codes with minimal shadow. As an
example, a singly even self-dual code with minimal shadow is
constructed for the first time. In addition, as neighbors of the code, we
construct singly even self-dual codes with weight enumerator for
which no singly even self-dual code was previously known to exist.Comment: 16 page
New MDS Self-dual Codes over Finite Fields of Odd Characteristic
In this paper, we produce new classes of MDS self-dual codes via (extended)
generalized Reed-Solomon codes over finite fields of odd characteristic. Among
our constructions, there are many MDS self-dual codes with new parameters which
have never been reported. For odd prime power with square, the total
number of lengths for MDS self-dual codes over presented in this
paper is much more than those in all the previous results