Relative one-weight linear codes

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Abstract

Relative one-weight linear codes were introduced by Liu and Chen over finite fields. These codes can be defined just as simply for egalitarian and homogeneous weights over Frobenius bimodule alphabets. A key lemma helps describe the structure of relative one-weight codes, and certain known types of two-weight linear codes can then be constructed easily. The key lemma also provides another approach to the MacWilliams extension theorem.

Communicated by R. Hill.
In memory of Professor F. E. P. Hirzebruch, 17 October 1927–27 May 2012.