Geodesic
The minimal circuits for linear Boolean functions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 41-44

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The paper is devoted to realization of linear Boolean functions by circuits of functional elements in the basis $\left\{x\ y, x\lor y, \overline{x}\right\}$. The main result is a structure description of the minimal circuits realizing linear Boolean functions. 
@article{VMUMM_2011_6_a8,
     author = {Yu. A. Kombarov},
     title = {The minimal circuits for linear {Boolean} functions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {41--44},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_6_a8/}
}
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Yu. A. Kombarov. The minimal circuits for linear Boolean functions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2011), pp. 41-44. http://geodesic.mathdoc.fr/item/VMUMM_2011_6_a8/