On the difficulty to beat the first linear programming bound for binary codes

Alex Samorodnitsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The first linear programming bound ([15]) is the best known asymptotic upper bound for binary codes, for a certain subrange of distances. Starting from the work of [7], there are, by now, some arguably easier and more direct arguments for this bound. We show that this more recent line of argument runs into certain difficulties if one tries to go beyond this bound (say, towards the second linear programming bound of [15]). Stated more constructively, we show that certain necessary requirements have to be met in order to produce a feasible solution to the dual linear program of [4] which improves on the first linear programming bound, following this line of argument.

Original languageEnglish
JournalIEEE Transactions on Information Theory
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

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