On A Class Of Asymptotically Good Codes

Thời gian: 14:00 đến 16:00 Ngày 24/06/2022

Địa điểm: C101, VIASM

Báo cáo viên: Bhanu Pratap Yadav

Tóm tắt:

Let $\mathbb F_{2}[u]=\mathbb F_{2}+u\mathbb F_{2}$, $u^2=0$. In this seminar, we construct a class of $\mathbb F_{2}[u]\mathbb F_{2}[u] $-additive cyclic codes generated by pairs of polynomials.~We discuss their algebraic structure and show that generator matrices can be obtained for all codes in this class. We study the asymptotic properties of this class of codes by using a Bernoulli random variable. Moreover, let $0 < \delta < 1$ be a real number and $k$ and $l$ be co-prime odd positive integers such that the entropy $h_{2}(\frac{(k+l)\delta}{4})<\frac{1}{2},$~ we show that the relative minimum distance converges to $\delta$ and the rates of the random codes converge to $\frac{1}{k+l}$. Finally, we conclude that the $\mathbb F_{2}[u]\mathbb F_{2}[u] $-additive cyclic codes are asymptotically good and provide some examples for this class of codes.