dc.contributor.author Al Kharoosi, Fatma Salim Ali dc.date.accessioned 2011-07-12T15:01:37Z dc.date.available 2011-07-12T15:01:37Z dc.date.issued 2011 dc.identifier.uri http://qmro.qmul.ac.uk/xmlui/handle/123456789/1312 dc.description PhD en_US dc.description.abstract For a quaternary code C of length n, de ne a pair of binary codes fC1;C2g en_US as: -C1 = C mod 2 -C2 = h(C \ 2Zn 4 ) where h is a bijection from 2Z4 to Z2 mapping 0 to 0 and 2 to 1 and for the extension to a map acting coordinatewise. Here C1 C2. For a pair of binary codes fC1;C2g with C1 C2, let C(C1;C2) be the set of Z4-codes giving rise to this binary pair as de ned above. Our main goal is to describe the set C(C1;C2) using the binary pair of codes fC1;C2g. In Chapter 1, we give some preliminaries. In Chapter 2, we start with a general description of codes fC1;C2g which give cardinality of C(C1;C2). Then we show that C(C1;C2) ' C 1 Zn 2 =C2. The cohomology of C(C1;C2) is given in Section (2:2). Then we end chapter 2 with a description of dual codes of C(C1;C2). Chapter 3 is about weight enumerators of codes in C(C1;C2). The average swe is given in terms of weight enumerators of C1 and C2 in Section(3:1) as swe(x; y; z) = jC2j 2n (weC1(x + z; 2y) 􀀀 (x + z)n) + weC2(x; z) Detailed computations of swe's of codes in C(C1;C2) using codes fC1;C2g is then given. Information about di erent weight enumerators of codes in C(C1;C2) is given in Section (3:2). These weight enumerators are included in an a ne space of polynomials. Then we end chapter 3 with a description of weight enumerators of self dual codes. Chapter 4 deals with actions of 2 the automorphism group G = Aut(C1) \ Aut(C2) Sn on C(C1;C2) which preserves cwe of codes. Corresponding action on C 1 Zn 2 =C2 is explained in this chapter. Changing signs of coordinates can be de ned as an action of Zn 2 on C(C1;C2). This action preserves swe of codes. Corresponding action on C 1 Zn 2 =C2 is provided in this chapter. In the appendix, we give a complete description of Z4-codes in C(C1;C2) with C1 = C2 = Extended Hamming Code of length 8. A programming code in GAP for computing derivations is given. And a description of the a ne space containing the swe's of Z4-codes is given with examples of di erent C1 = C2 having same weight enumerator. dc.description.sponsorship Sultan Qaboos University and the government of the Sultanate Oman providing the scholarship. dc.language.iso en en_US dc.subject Mathematics en_US dc.title Describing quaternary codes using binary codes en_US dc.type Thesis en_US dc.rights.holder The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author
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Theses Awarded by Queen Mary University of London