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By Mazurov V.D.

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The valency of the vertex x is the cardinality of its star. A morphism p W X ! Y is called locally injective if the restriction of p to the star of any vertex of X is injective. A graph X is called oriented if in each pair of its mutually inverse edges fe; eg N one edge is chosen. This edge is called positively oriented and the other is called negatively oriented. The set of all positively (negatively) oriented edges is denoted 1 1 (respectively X 1 ). The set XC is called an orientation of the graph X .

The set of all positively (negatively) oriented edges is denoted 1 1 (respectively X 1 ). The set XC is called an orientation of the graph X . by XC Graphs can be drawn as objects consisting of points and lines which connect some of these points. The lines correspond to pairs of inverse edges. Positively oriented edges will be drawn as lines with arrows. n 2 Z, n > 1/ and C1 . ei / D i C 1 (the addition is modulo n). ei / D i C 1 (Figure 3). eiC1 /, i D 1; : : : ; n 1. en / are the beginning and the end of l.

N; m/-code, where m D dim C . The automorphism group of a linear code C Â F n is the group of all linear transformations of the vector space F n permuting the standard8 basis vectors ei , i D 1; : : : ; n; and preserving the subspace C . c1 ; : : : ; cn / 2 C; ci D 0 iD0 lying in F nC1 . 2) Let k > 1, n D 2k 1. n; n k/code C D fu 2 F n j uH D 0g, where H is a matrix of size n k whose rows are all nonzero vectors of the space F k written in some order. From this it follows that the weight of any nonzero word from C is at least 3, and hence C is an 1-code.

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