Uniqueness of the ( 22 , 891 , 1 / 4 ) spherical code Henry Cohn and

Henry Cohn and Abhinav Kumar

We use techniques of Bannai and Sloane to give a new proof that there is a unique (22, 891, 1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23, 4600, 1/3) spherical code.

متن کامل

Uniqueness of the (22,891, 1/4) Spherical Code

We use techniques of Bannai and Sloane to give a new proof that there is a unique (22, 891, 1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23, 4600, 1/3) spherical code. An (n, N, t) spherical code is a set of N points on the unit sphere S n−1 ⊂ R n such that no two distinct poi...

متن کامل

. M G ] 9 S ep 2 00 8 THE D 4 ROOT SYSTEM IS NOT UNIVERSALLY OPTIMAL

We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a constr...

متن کامل

The D 4 Root System Is Not Universally Optimal

We prove that the D4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S, based on numerical computations suggesting that every 5-design consisting of 24 points in S is in a 3-parameter family (which we describe explicitly, based on a constr...

متن کامل

Rigidity of spherical codes

A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configurati...

متن کامل

Uniqueness of the ( 22 , 891 , 1 / 4 ) spherical code Henry Cohn and

نویسندگان

چکیده

منابع مشابه

Henry Cohn and Abhinav Kumar