Geodesic
The threshold effect for systems of random equations of a special type
Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 29-39.

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The results on the threshold effect obtained previously (see [BKKh,RSA]) for systems of linear equations in $\GF(2)$ are extended to the finite prime fields $\GF(\,p)$ with $p\geq 3$.The work is partially supported by the Russian Foundation for Fundamental Investigations, Grant 93–011–1443. 
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V. F. Kolchin; V. I. Khokhlov. The threshold effect for systems of random equations of a special type. Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 29-39. http://geodesic.mathdoc.fr/item/DM_1995_7_4_a1/