Geodesic
On complexity of realisation of linear Boolean functions by circuits of functional elements over the basis
Diskretnaya Matematika, Tome 15 (2003) no. 4, pp. 100-112

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We show that the minimal circuit of functional elements over the basis $\{x\to y,\bar x\}$ which realises a linear function of $n$ variables consists of $4n-4$ elements. 
@article{DM_2003_15_4_a5,
     author = {I. C. Shkrebela},
     title = {On complexity of realisation of linear {Boolean} functions by circuits of functional elements over the basis},
     journal = {Diskretnaya Matematika},
     pages = {100--112},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2003_15_4_a5/}
}
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I. C. Shkrebela. On complexity of realisation of linear Boolean functions by circuits of functional elements over the basis. Diskretnaya Matematika, Tome 15 (2003) no. 4, pp. 100-112. http://geodesic.mathdoc.fr/item/DM_2003_15_4_a5/