[Turkmath:5640] İ.Ü. Matematik Bölüm Semineri

[TEMHA ERKOÇ YILMAZTÜRK]

Merhabalar,

25.05.2022  tarihinde  saat 14.00 te  Balıkesir Üniversitesinden Doç. Dr.
Seher Tutdere  başlık ve özeti aşağıda verilen bir konuşma yapacaktır.
Seminer Zoom programı üzerinden online yapılacaktır. Katılmak isteyenlerin
katılım bilgilerini alabilmeleri için "huseyinuysal at istanbul.edu.tr "
adresine mail atmaları gerekmektedir.


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*Başlık:* ON THE COVERING RADII OF CYCLIC CODES OVER BINARY FINITE FIELDS

*Özet:*Let F_2 denote the finite field of two elements. An [n,k]  binary
linear block code C is a k-dimensional subspace of F_2^n. For u,v∈F_2^n,
let d(u,v) denote the number of coordinate places where u and v differ,
which is called the Hamming distance between u and v. The covering radius
of a block code C of length n is the smallest integer R=R(C) such that all
vectors in the containing space are within Hamming distance R of some
codeword of C. Equivalently, the covering radius of C  is the smallest
integer R such that every q-ary (n −k) tuple can be written as a linear
combination of at most R columns of the parity-check matrix of C. There has
been an intense interest in covering radius since a paper of Delsarte in
1973. It has applications to problems of data compression, testing, and
write-once memories etc. Computing the covering radius of a given code is a
hard task. Cyclic codes are one of the most commonly used class of linear
block codes, where the circular shifts of each codeword gives another word
that belongs to the code. They have a rich algebraic structure which are
useful for efficient error detection and correction. In this talk, we will
mention from some results regarding the  covering radii of cyclic codes
over binary finite fields.

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İyi Günler dilerim.
Temha

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