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Line 78: ==Bonisoli's theorem== A code is defined to be '''equidistant''' if and only if there exists some constant ''d'' such that the distance between any two of the code's distinct codewords is equal to ''d''.<ref>{{cite ~~journal~~arxiv\|author=Etzion, Tuvi\|author2=Raviv, Netanel\|title=Equidistant codes in the Grassmannian~~\|journal=arXiv preprint arXiv:1308.6231~~\|year=2013\|~~url~~arxiv=~~https://arxiv.org/abs/~~1308.6231}}</ref> In 1984 Arrigo Bonisoli determined the structure of linear one-weight codes over finite fields and proved that every equidistant linear code is a sequence of [[w:Dual code\|dual]] [[Hamming code]]s.<ref>{{cite journal\|author=Bonisoli, A.\|year=1984\|title=Every equidistant linear code is a sequence of dual Hamming codes\|journal=Ars Combinatoria\|volume=18\|pages=181–186}}</ref>. ==Examples==

Linear code: Difference between revisions