On Sets of Ternary Vectors Whose Only Linear Dependencies Involve an Odd Number of Vectors
Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 363-366
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Recent efforts to generalize a classic result of Hajos [3] on the decomposition of finite abelian groups into direct sums of subsets (see Fuchs [1, Chap. XV]) led B. Gordon [2] to the following conjecture. If are r-dimensional row vectors over GF(3) such that: (i) Any weighted (±) sum of any even number of 's is nonzero, (ii) For each r-dimensional , there exists an s such that Then there exists a subset of either 1 or 4 's which satisfies the same conditions.This paper proves Gordon's conjecture.
Berlekamp, E. R. On Sets of Ternary Vectors Whose Only Linear Dependencies Involve an Odd Number of Vectors. Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 363-366. doi: 10.4153/CMB-1970-068-8
@article{10_4153_CMB_1970_068_8,
author = {Berlekamp, E. R.},
title = {On {Sets} of {Ternary} {Vectors} {Whose} {Only} {Linear} {Dependencies} {Involve} an {Odd} {Number} of {Vectors}},
journal = {Canadian mathematical bulletin},
pages = {363--366},
year = {1970},
volume = {13},
number = {3},
doi = {10.4153/CMB-1970-068-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-068-8/}
}
TY - JOUR AU - Berlekamp, E. R. TI - On Sets of Ternary Vectors Whose Only Linear Dependencies Involve an Odd Number of Vectors JO - Canadian mathematical bulletin PY - 1970 SP - 363 EP - 366 VL - 13 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-068-8/ DO - 10.4153/CMB-1970-068-8 ID - 10_4153_CMB_1970_068_8 ER -
%0 Journal Article %A Berlekamp, E. R. %T On Sets of Ternary Vectors Whose Only Linear Dependencies Involve an Odd Number of Vectors %J Canadian mathematical bulletin %D 1970 %P 363-366 %V 13 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-068-8/ %R 10.4153/CMB-1970-068-8 %F 10_4153_CMB_1970_068_8
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