Cocyclic Hadamard codes

We demonstrate that many well-known binary, quaternary, and q-ary codes are cocyclic Hadamard codes; that is, derived from a cocyclic generalized Hadamard matrix or its equivalents. Nonlinear cocyclic Hadamard codes meet the generalized Plotkin bound. Using presemifield multiplication cocycles, we construct new equivalence classes of cocyclic Hadamard codes which meet the Plotkin bound.

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