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Abstract:

In this paper, we present numerical upper bounds on the sizes of constrained codes with a prescribed minimum distance. We accomplish this by extending Delsarte's linear program (LP) (Delsarte (1973)) to the setting of constrained codes, with the value of optimal solutions to this LP giving us the desired upper bound, for a fixed constraint. We also describe an equivalent LP, with fewer variables and LP constraints, obtained by symmetrizing our LP. We observe that for different constraints of interest, our upper bounds beat the generalized sphere packing upper bounds of Fazeli, Vardy, and Yaakobi (2015).