Unique optima of the Delsarte linear program

Abstract The Delsarte linear program is used to bound the size of codes given their block length n and minimal distance d by taking a relaxation from quasicodes. We study for which values ( , ) this has unique optimum: while we show that it does not always have optimum, prove if $$d>n/2$$ d > n / 2 or $$d \le 2$$ ≤ . Introducing Krawtchouk decomposition quasicode, there exist optima 2 e $$(n-1,2e-1)$$ ( - 1 , e ) programs essentially identical decompositions, revealing parity phenomenon among programs. generalize notion extending puncturing quasicodes, see relationship extending/puncturing. further characterize these pairs optima, in particular demonstrating they exhibit symmetry property, effectively halving number decision variables.