Name
Abstract | ||
|---|---|---|
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a Reed–Solomon code of small field size and with the same minimum distance. In particular, if the code has length
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>
, and maximum minimum distance
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>
(over all generator matrices with the given support), then an optimal code exists for any field size
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q\geq 2n-d$ </tex-math></inline-formula>
. As a by-product of this result, we settle the GM–MDS conjecture in the affirmative. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/TIT.2019.2932663 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
Generators,Linear codes,Upper bound,Relays,Silicon | Discrete mathematics,Combinatorics,Generator matrix,Computer science,Conjecture | Journal |
Volume | Issue | ISSN |
65 | 12 | 0018-9448 |
Citations | PageRank | References |
1 | 0.37 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hikmet Yildiz | 1 | 4 | 2.84 |
| Babak Hassibi | 2 | 8737 | 778.04 |