60th anniversary of the discovery of Golay code

The probably most interesting code was introduced by Golday sixty years ago in half a page:

Golay, M. J. E. "Notes on Digital Coding." Proc. IRE 37, p.657, 1949.

http://mathworld.wolfram.com/GolayCode.html

http://en.wikipedia.org/wiki/Binary_Golay_code

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Nowaday, is it possible to write an influential one-page article? or even, have a one-page article successfully published?

Upper bound on size of conflict-avoiding code

40th birhtday of Internet

History of the Internet
http://www.youtube.com/watch?v=hAtDqBJFxsc

LP bound on size of code using Matlab

% Linear programming bound on the size of a nonlinear q-ary code
% of length n and minimum distance d

% Inputs:
q = 2;  % alphabet size
n = 16;  % code length
d = 6;  % minimum distance

% Compute the values of Krawtchouck polynomial
K = zeros(n-1,n);
c = zeros(n-1,1);
for k = 1:(n-1)
  for w = 1:n
    for j = max(0,(k-n+w)):min(w,k)
      K(k,w) = K(k,w)+(-1)^j*(q-1)^(k-j)*nchoosek(w,j)*nchoosek(n-w,k-j);
    end
  end
  c(k) = (q-1)^(k)*nchoosek(n,k);
end

% Linear Programming
x = linprog(-ones(1,n-d+1),-K(:,d:end),c,[],[],zeros(1,n-d+1));

% Output: upper bound on number of codewords
1+floor(sum(x+1e-8))

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Nordstrom-Robinson code's  parameters q=2, n=16, d=6 are used in the example.

Matab program for calculating the Oesterle bound

% Oesterle bound on the number of rational points
%    of algebraic curve over finite field

% Inputs
q = 2;   % size of fintie field
g = 18;  % genus

% Weil's upper bound on number of rational points
WB = 1+q+g*floor(2*sqrt(q));

for N = WB:-1:3
    lambda = N-1;
    alpha=sqrt(q);  
    m = floor(log(lambda)/log(alpha));
    u = ( alpha^(m+1) - lambda ) / (lambda*alpha - alpha^m );
    x = fzero(@(x) cos(x*(m+1)/2)/cos(x*(m-1)/2)+u,pi/(m+1));
    if x<=pi/m && x >= pi/(m+1)    % verify that x is between pi/(m+1) and pi/m
        if ((lambda-1)*alpha*cos(x) + alpha^2-lambda ) / ...
                (alpha^2 - 2*alpha*cos(x) + 1)  <  g
            break
        end
    else
        disp('error in solving for x')
    end
end

% Output: 
% Upper bound on number rational points for curve with genus g over GF(q)
N