ABSTRACT. We connect two nonlinear irreducible character of a finite group G if their degrees have a common prime divisor. In this paper we show that the corresponding graph has at most three connected components.
Commonly, the direct construction and the description of mutually orthogonal Latin squares (MOLS) make use of difference or quasi‐difference matrices. Now there exists a correspondence between MOLS and separable permutation codes. We present separable permutation codes of length
35,
48,
63, and
96 and minimum distance
34,
47,
62, and
95 consisting of
6
goodbreakinfix×
35,
10
goodbreakinfix×
48,
8
goodbreakinfix×
63, and
8
goodbreakinfix×
96 codewords, respectively. Using the correspondence, this gives 6 MOLS for
n
goodbreakinfix=
35,
10 MOLS for
n
goodbreakinfix=
48,
8 MOLS for
n
goodbreakinfix=
63, and
8 MOLS for
n
goodbreakinfix=
96. The codes are given by generators of an appropriate subgroup
U of the isometry group of the symmetric group
S
n and
U‐orbit representatives. This gives an alternative uniform way to describe the MOLS.
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