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(Solved): Theorem 1.7.6 Let C be a code over F_(q). The following hold: (i) If M is a monomial matrix with ent ...



Theorem 1.7.6 Let

C

be a code over

F_(q)

. The following hold: (i) If

M

is a monomial matrix with entries only from

{0,-1,1}

, then

C

is self-dinal if and only if CM is self-dual.

C~=C_(1)

c=c^(2)<=>c_(1)=c_(1)^(-)

(ii) If

q=3

and

C

is equivalenti to

C_(1)

, then

C

is self-dual if and only if

C_(1)

is self-dual. (iii) If

q=4

and

C

is equivalent to

C_(1)

/then

C

is Hermitian self-dual if and only if

C_(1)

is Hermitian self-dinal.

c=c^(2 1)<=>c_(1)=c^(2 1)


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