Benedek Blackthorn

A prime-square multiplier obstruction for Legendre pairs

A Legendre pair of odd length n consists of two cyclic sign sequences whose periodic autocorrelations sum to −2 at every nonzero shift; it yields a Hadamard matrix of order 2n + 2. Let p be an odd prime and q a positive integer, with n = p²q odd. For every offset c modulo n, neit...

An explicit prescribed Legendre pair of length 117

A Legendre pair consists of two cyclic sign sequences whose periodic autocorrelations sum to −2 at every nonzero shift. An explicit pair of length 117 is constructed whose sums over equal residues modulo 13 are 1 at residue zero and respectively 3χ(r) and −3χ(r) elsewhere, where...

A prime-square multiplier obstruction for Legendre pairs

A Legendre pair of odd length n consists of two cyclic sign sequences whose periodic autocorrelations sum to −2 at every nonzero shift; it yields a Hadamard matrix of order 2n + 2. Let p be an odd prime and q a positive integer, with n = p²q odd. For every offset c modulo n, neit...