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Small orders of Hadamard matrices and base sequences
Dragomir Z. Djokovic
We update the list of odd integers n<10000 for which an Hadamard matrix of order 4n is known to exist. We also exhibit the first example of base sequences BS(40,39). Consequently,…
Classification of normal sequences
Dragomir Z. Djokovic
Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, with A and B of length m and C and D of length n, such that the sum of their nonperiodic autocorrelation funct…
A new Yang number and consequences
Dragomir Z. Djokovic
Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, A and B of length m and C and D of length n, the sum of whose non-periodic auto-correlation functions is zero.…
Generalized distillability conjecture and generalizations of Cauchy-Bunyakovsky-Schwarz inequality and Lagrange identity
Dragomir Z. Djokovic
Let rho_k, k=1,2,...,m, be the critical Werner state in a bipartite d_k by d_k quantum system, i.e., the one that separates the 1-distillable Werner states from those that are 1-in…
On two-distillable Werner states
Dragomir Z. Djokovic
We consider bipartite mixed states in a quantum system. We say that is PPT if its partial transpose is positive semidefinite, and otherwise i…
Hadamard matrices from base sequences: An example
Dragomir Z. Djokovic
There are several well-known methods that one can use to construct Hadamard matrices from base sequences BS(m,n). In view of the recent classification of base sequences BS(n+1,n) f…