Published December 2019
| public
Journal Article
Optimum Linear Codes with Support-Constrained Generator Matrices over Small Fields
- Creators
-
Yildiz, Hikmet
-
Hassibi, Babak
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 n, and maximum minimum distance d (over all generator matrices with the given support), then an optimal code exists for any field size q ≥ 2n-d. As a by-product of this result, we settle the GM–MDS conjecture in the affirmative.
Additional Information
© 2019 IEEE. Manuscript received September 24, 2018; revised May 25, 2019; accepted July 16, 2019. Date of publication August 2, 2019; date of current version November 20, 2019. This work was supported in part by the National Science Foundation under Grant CNS-0932428, Grant CCF-1018927, Grant CCF-1423663, and Grant CCF-1409204, in part by Qualcomm Inc., in part by the NASAs Jet Propulsion Laboratory through the President and Directors Fund, and in part by the King Abdullah University of Science and Technology. This article was presented in part at the International Symposium on Information Theory and at the Information Theory Workshop.Additional details
- Eprint ID
- 97900
- Resolver ID
- CaltechAUTHORS:20190814-151834005
- CNS-0932428
- NSF
- CCF-1018927
- NSF
- CCF-1423663
- NSF
- CCF-1409204
- NSF
- Qualcomm Inc.
- JPL President and Director's Fund
- King Abdullah University of Science and Technology (KAUST)
- Created
-
2019-08-15Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field