Steiner triple systems of order 15 and their codes

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The binary linear codes generated by incidence matrices of the 80 Steiner triple systems on 15 points (STS(15)) are studied. The 80 codes of length 35 spanned by incidence vectors of the points are all non-isomorphic. In contrast, a pair of codes of length 15 generated by blocks are isomorphic if and only if the corresponding incidence matrices have the same rank over GF(2). The weight distribution, the automorphism groups of the codes, and the distribution of the Steiner triple systems within the codes are computed. There are 54 codes of length 35 that contain several non-isomorphic STS(15)'s, and any such code is generated by an STS(15) of largest 2-rank.

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Copyright © 1997 Published by Elsevier B.V. Publisher’s version of record: https://doi.org/10.1016/S0378-3758(96)00071-7

Publication Title

Journal of Statistical Planning and Inference