Abstracts

In this thesis some constructions of superimposed codes are presented. Many of the known nontrivial constructions arise from tdesigns, and the constructions discussed in this thesis is also based on a block design idea. Superimposed codes are rather combinatorial in nature, so the connection to tdesigns is not too surprising. What may be a little surprise, however, is the connection between superimposed codes and linear codes and Galois elds. Linear codes are quite intuitive and have nice properties, as is the case for Galois elds; combinatorial structures are quite often the contrary, not intuitive and quite dicult to understand. Because of this, it is interesting that a combinatorial structure like superimposed codes can be constructed from structures like linear codes and Galois elds. The main goal of this thesis is to present two possibly new approaches to construct superimposed codes. The constructions are described, but not proved to be correct. The rst construction presented is using graphs. In practice, this is not a good way to construct codes, since it requires the construction of a graph and nding certain cycles in the graph. It is still an interesting construction, however, since it provides a connection between constant weight codes and superimposed codes. Another construction is presented, one that seems much more useful when constructing codes. In [7] one particular superimposed code is constructed from a Galois eld. In this thesis we will see that this construction using Galois elds can be generalized. I denna uppsats presenteras ngra konstruktioner av verlagrade koder. Mnga av de redan knda konstruktionerna har sitt ursprung i t-designer, och ven konstruktionerna som behandlas i denna uppsats r baserade p en blockdesignsid. verlagrade koder r tmligen kombinatoriska till sin natur, s kopplingen mellan verlagrade koder och t-designer r inte speciellt verraskande. Dremot kan kopplingen mellan verlagrade koder, linjra koder och Galoiskroppar vara verraskande. Linjra koder r ganska intuitiva och har trevliga egenskaper, likas Galoiskroppar; kombinatoriska strukturer r ofta tvrt om, inte intuitiva och svra att frst. P grund av detta r det intressant att kombinatoriska strukturer som verlagrade koder kan konstrueras med hjlp av strukturer som linjra koder och Galoiskroppar. Det primra mlet med denna uppsats r att presentera tv mjligen nya konstruktioner av verlagrade koder. Konstruktionerna beskrivs men deras korrekthet bevisas inte. Den frsta konstruktionen som presenteras r baserad p grafer. I praktiken r denna konstruktionen inte bra fr att skapa koder, eftersom den krver konstruktion av en graf och sedan att hitta vissa cykler i grafen. Det r dock fortfarande en intressant konstruktion, eftersom den bidrar till en intressant koppling mellan konstantvikt koder och verlagrade koder. En annan konstruktion presenteras, och den r mycket mer praktiskt anvndbar. I [7] skapas en specik verlagrad kod med hjlp av en Galoiskropp. I denna uppsats ser