The paper gives a matrix-free presentation of the correspondence between full-length linear codes and projective multisets. It generalizes the Brouwer-Van Eupen construction that transforms projective codes into two-weight codes. Short proofs of known theorems are obtained. A new notion of self-duality in coding theory is explored.
Abstract. Recently Jungnickel and Tonchev have shown that there exist at least four inequivalent binary selfcomplementary [28,7,12] codes and have asked if there are other [28,7] codes with weight distribution A 0 = A28 = 1, A12 = AI6 = 63. In the present paper we give a negative answer: these four codes are, up to equivalence, the only codes with the given parameters. Their residuals are also classified.
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