منابع مشابه
On cyclic codes of composite length and the minimal distance
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and dimension over the same finite field. However, not much is known about these codes. In this paper we explain some of the mysteries of the numerical data by ...
متن کاملNumber of minimal cyclic codes with given length and dimension
In this article, we count the quantity of minimal cyclic codes of length n and dimension k over a finite field Fq, in the case when the prime factors of n satisfy a special condition. This problem is equivalent to count the quantity of irreducible factors of x − 1 ∈ Fq[x] of degree k.
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We describe an algorithm that improves on the standard algorithm for computing the minimal distance of cyclic codes.
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We consider binary abelian codes of length pq where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.
متن کاملSkew cyclic codes of arbitrary length
In this paper we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalization of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2012
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2012.07.003