We propose and test a new linearisation technique for the Binary Quadratic Problems (BQPs). We computationally prove that the new formulation, called Extended Linear Formulation, can be effective for different classes of problems in practice. Our tests are based on two sets of classical BQPs from the literature, i.e., the Unconstrained BQP and the Maximum Cut of edge-weighted graphs. Finally we...

A construction based on Legendre sequences is presented for a doubly-extended binary linear code of length 2p + 2 and dimension p+1. This code has a double circulant structure. For p = 4k +3, we obtain a doubly-even self-dual code. Another construction is given for a class of triply extended rate 1/3 codes of length 3p + 3 and dimension p + 1. For p = 4k + 1, these codes are doubly-even selfort...