An irreducible cyclic (n, k) code is said to be semiprimitive if n = (2 k -l)/N where N> 2 divides 2 j + 1 for some j ~1. The complete weight hierarchy of the semiprimitive codes is determined when k/2j is odd. In the other cases, when k/2j is even, some partial results on the generalized Hamming we
The weight hierarchy of the Kasami codes
β Scribed by Tor Helleseth; P Vijay Kumar
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 413 KB
- Volume
- 145
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
The Kasami codes is a family of [2 2m --1, 3m, 2 TM 1 _ 2"-1 ] codes which are well known for their applications to construct sequences with optimal correlation magnitudes. The weight hierarchy of the Kasami codes is completely determined. It is also shown that the chain condition holds for these codes.
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The number of words of weight w in the product code of linear codes with minimum distances d, and d, is expressed in the number of low weight words of the constituent codes, provided that w <d,d, + max(d,, d<). By examples it is shown that, in general, the full weight enumerator of a product code is