TY - JOUR
T1 - On the difficulty to beat the first linear programming bound for binary codes
AU - Samorodnitsky, Alex
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85210390302&partnerID=8YFLogxK
U2 - 10.1109/TIT.2024.3504268
DO - 10.1109/TIT.2024.3504268
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AN - SCOPUS:85210390302
SN - 0018-9448
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
ER -