منابع مشابه
Cyclic self-dual codes
Ahstruct-It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial code in this class is shown to hav...
متن کاملCyclic Codes and Self-Dual Codes Over
We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u = 0 and study them by analogy with the Z4 case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z4-codes. Unlike the Z4 case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-d...
متن کاملIsometrically Self-dual Cyclic Codes
General isometries of cyclic codes, including multipliers and translations, are introduced; and isometrically self-dual cyclic codes are defined. In terms of Type-I duadic splittings given by multipliers and translations, a necessary and sufficient condition for the existence of isometrically selfdual cyclic codes is obtained. A program to construct isometrically selfdual cyclic codes is provid...
متن کاملCyclic Codes and Self-Dual Codes Over F2 + uF2
We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u 2 = 0. This ring shares many properties of Z 4 and F 4 and admits a linear "Gray map". Cyclic codes are described as modules over (F 2 + uF 2) n which may not be free. Self-dual codes of odd length exists as in the case of Z 4-codes. We exhibit some extremal codes of this very interesting family.
متن کاملGood self-dual quasi-cyclic codes exist
We show that there are long binary quasi-cyclic self-dual (either Type I or Type II) codes satisfying the Gilbert–Varshamov bound.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 1997
ISSN: 1071-5797
DOI: 10.1006/ffta.1996.0172