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The condition for a cyclic code to have a complementary dual

โœ Scribed by Xiang Yang; James L. Massey

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
145 KB
Volume
126
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

A linear code with a complementary dual (an LCD code) is a linear code C whose dual code Cl satisfies CnC'= (0). It is shown that the necessary and sufficient condition for a cyclic code C of length n to be an LCD code is that the generator polynomial g(x) of C be self-reciprocal and all the manic irreducible factors of g(x) have the same multiplicity in g(x) as in x"-1.

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