| 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
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. | en_US |
| 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 | |
