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We call a linear code C with length n over a field F, a linear complementary equi-dual code, when there exists a linear code D over F such that D is permutation equivalent to C^ and (C, D) is a linear complementary pair of codes, that is, C+ D=Fⁿ and C D=0. We first state a necessary condition on a code C to be linear complementary equi-dual. Then, we conjecture that this necessary condition is also sufficient and present several statements which support this conjecture.
Nikseresht et al. (Sat,) studied this question.