2 research outputs found
Quasi-Perfect and Distance-Optimal Codes Sum-Rank Codes
Constructions of distance-optimal codes and quasi-perfect codes are
challenging problems and have attracted many attentions. In this paper, we give
the following three results.
1) If and , an infinite family of
distance-optimal -ary cyclic sum-rank codes with the block length
, the matrix size , the cardinality
and the minimum sum-rank distance four is constructed.
2) Block length and the matrix size distance-optimal
sum-rank codes with the minimum sum-rank distance four and the Singleton defect
four are constructed. These sum-rank codes are close to the sphere packing
bound , the Singleton-like bound and have much larger block length
.
3) For given positive integers satisfying , an infinite family
of quasi-perfect sum-rank codes with the matrix size , and the
minimum sum-rank distance three is also constructed. Quasi-perfect binary
sum-rank codes with the minimum sum-rank distance four are also given.
Almost MSRD -ary codes with the block lengths up to are given. We
show that more distance-optimal binary sum-rank codes can be obtained from the
Plotkin sum.Comment: 19 pages, only quasi-perfect sum-rank codes were constructed. Almost
MSRD codes with the block lengths up to were include