## Abstract A (__w,r__) __coverβfree family__ is a family of subsets of a finite set such that no intersection of __w__ members of the family is covered by a union of __r__ others. A __binary__ (__w,r__) __superimposed code__ is the incidence matrix of such a family. Such a family also arises in cr
Uniqueness of some optimal superimposed codes
β Scribed by S. Hong; S. Kapralov; H. K. Kim; D. Y. Oh
- Book ID
- 110179749
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2007
- Tongue
- English
- Weight
- 387 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0032-9460
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## Abstract A (__w__,__r__) __coverβfree family__ is a family of subsets of a finite set such that no intersection of __w__ members of the family is covered by a union of __r__ others. A (__w__,__r__) __superimposed code__ is the incidence matrix of such a family. Such a family also arises in crypt
We continue here the research on (quasi)group codes over (quasi)group rings. We give some constructions of [n, n -3, 3] qcodes over F q for n = 2q and n = 3q. These codes are linearly optimal, i.e. have maximal dimension among linear codes having a given length and distance. Although codes with such