Arithmetic constructions of binary self-dual codes.

Format:

Book

Thesis/Dissertation

Author/Creator:

Zhang, Ying.

Contributor:

Towsner, Henry, committee member.

Pop, Florian, 1952- committee member.

Chinburg, Ted, 1954- committee member.

Chinburg, Ted, 1954- advisor.

University of Pennsylvania. Mathematics.

Language:

English

Subjects (All):

Mathematics.

Applied mathematics.

0364.

0405.

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

0364.

0405.

Physical Description:

92 pages

Contained In:

Dissertation Abstracts International 75-01B(E).

System Details:

Mode of access: World Wide Web.

text file

Summary:

The goal of this thesis is to explore the interplay between binary self-dual codes and the etale cohomology of arithmetic schemes. Three constructions of binary self-dual codes with arithmetic origins are proposed and compared: Construction Q , Construction G and the Equivariant Construction. In this thesis, we prove that up to equivalence, all binary self-dual codes of length at least 4 can be obtained in Construction Q . This inspires a purely combinatorial, non-recursive construction of binary self-dual codes, about which some interesting statistical questions are asked. Concrete examples of each of the three constructions are provided. The search for binary self-dual codes also leads to inspections of the cohomology "ring" structure of the etale sheaf mu2 on an arithmetic scheme where 2 is invertible. We study this ring structure of an elliptic curve over a p-adic local field, using a technique that is developed in the Equivariant Construction.

Notes:

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2013.

Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.

Adviser: Ted Chinburg.

Local Notes:

School code: 0175.

ISBN:

9781303397042

Access Restriction:

Restricted for use by site license.