Geodesic
Easily tested circuits for linear functions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 57-59

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It is shown that a linear Boolean function of $n$ variables can be realized over the basis $\{\,\vee,\;\bar{ }\;\}$ by an unzedundant circuit admitting a unit diagnostic test of the length $]\log (n-1)[ \;+2$ for inverse output errors of elements. 
@article{VMUMM_2011_4_a11,
     author = {S. R. Bedzhanova},
     title = {Easily tested circuits for linear functions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {57--59},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a11/}
}
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S. R. Bedzhanova. Easily tested circuits for linear functions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 57-59. http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a11/