turkmath.org

The birth of coding theory was inspired by the seminal paper of Claude Shannon “A Mathematical Theory of Communication”, which was published in 1948. In this talk, I will mention some basic concepts of coding theory such as error detection, correction and decoding. Then I will present linear codes together with their structure and properties. A linear code of length $n$ over the finite field $\mathbb{F}_q$ is a subspace of the vector space $\mathbb{F}^n_q$. I will introduce self-dual codes which are a special subclass of linear codes. Self-dual codes are important because many of the best codes known are of this type. Finally, I will conclude my speech by talking about weights and Gray maps.