Covering radius for codes obtained from T(m) triangular graphs
Triangular graphs are a special case of the well-known strongly regular graphs.
Taking any spanning tree in a T(m) triangular graph -m≥4- we get a fundamental circuit matrix for it. Using this matrix as a generator matrix we can obtain a single-error-correcting linear code C(T(m)) with parameters:
n=(m(m−1) (m−2))/2, k=(m(m−1) (m−3)+2)/2 and d=3.
whatever the value of m be, if we take a hamiltonian path as a spanning tree in T(m), the obtained code C(T(m)) has covering radius σ equal to [m(m−1)/4] and
fixed m all the C(T(m)) codes are equivalent independently of the chosen spanning tree,
so, it is finally proved that given T(m) and any spanning tree in it, C(T(m)) has σ=[m(m−1)/4].
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