311 citations · 1.2k across the 55 of their papers we have counts for
5 papers · 1 filter
New upper bounds on sphere packings I
Henry Cohn, Noam Elkies
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which ar…
On finite sequences satisfying linear recursions
Noam D. Elkies
For any field k and any integers m,n with 0 <= 2m <= n+1, let W_n be the k-vector space of sequences (x_0,...,x_n), and let H_m be the subset of W_n consisting of the sequences tha…
Excellent nonlinear codes from modular curves
Noam D. Elkies
We introduce a new construction of error-correcting codes from algebraic curves over finite fields. Modular curves of genus g -> infty over a field of size q0^2 yield nonlinear cod…
Explicit modular towers
Noam D. Elkies
We give a general recipe for explicitly constructing asymptotically optimal towers of modular curves such as {X_0(l^n): n=1,2,3,...}. We illustrate the method by giving equations f…
On the sums Sum((4k+1)^(-n),k,-inf,+inf)
Noam D. Elkies
The sum in the title is a rational multiple of pi^n for all integers n=2,3,4,... for which the sum converges absolutely. This is equivalent to a celebrated theorem of Euler. Of the…