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We introduce a new class of complex Hadamard matrices which have not been studied previously. We use these matrices to construct a new infinite family of parity proofs of the Kochen-Specker theorem. We show that the recently discovered simple parity proof of the Kochen-Specker theorem is the initial member of this infinite family. [ABSTRACT FROM AUTHOR]

Abstract: Steganography is concerned with communicating hidden messages in such a way that no one apart from the sender and the intended recipient can detect the very existence of the message. We study the syndrome coding method (sometimes also called the “matrix embedding method”), which uses a linear code as an ingredient. Among all codes of a fixed block length and fixed dimension (and thus of a fixed information rate), an optimal code is one that makes it most difficult for an eavesdropper to detect the presence of the hidden message. We show that the average distance to code is the appropriate concept that replaces the covering radius for this particular application. We completely classify the optimal codes in the cases when the linear code used in the syndrome coding method is a one- or two-dimensional code over . In the steganography application this translates to cases when the code carries a high payload (has a high information rate). [Copyright &y& Elsevier]