1 research outputs found
The Weight Distribution of Quasi-quadratic Residue Codes
In this paper, we begin by reviewing some of the known properties of QQR
codes and proved that acts on the extended QQR code when . Using this discovery, we then showed their weight polynomials satisfy
a strong divisibility condition, namely that they are divisible by , where is the corresponding minimum distance. Using this
result, we were able to construct an efficient algorithm to compute weight
polynomials for QQR codes and correct errors in existing results on quadratic
residue codes.
In the second half, we use the relation between the weight of codewords and
the number of points on hyperelliptic curves to prove that the symmetrized
distribution of a set of hyperelliptic curves is asymptotically normal.Comment: submitted to AIM