Conference-matrix MDS code conjecture

Let pp be a prime, and let C{\mathbb C} be a code of length p+1p+1 constructed from a generator matrix that is a conference matrix. Conference-matrix MDS conjecture. The code C{\mathbb C} is an MDS code of dimension p+12\frac{p+1}{2} and minimum Hamming distance p+32\frac{p+3}{2}. This would give an MDS code with parameters determined by the rank of a conference matrix over Zp{\mathbb Z}_p; the source provides no resolution of the claim.

Sources & referencesView supporting material

Primary source

Tuvi Etzion, Alexander Vardy and Eitan Yaakobi, “Coding for the Lee and Manhattan Metrics with Weighing Matrices”, arXiv:1210.5725 (2012).

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