Ressource pédagogique : 1.3. Encoding (Linear Transformation)

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Description (résumé)

In this session, we will talk about the easy map of the  - one-way trapdoor functions based on error-correcting codes. We suppose that the set of all messages that we wish to transmit is the set of k-tuples having elements from the field Fq. There are qk possible messages and we referred to it as the message space.  In order to detect and possibly correct errors, we add some redundancy, thus the k tuples will be embedded into n-tuples with n greater than k. In this MOOC, we will focus on linear encoder that is linear transformations. Every linear transformation can be represented by a matrix multiplication. Thus our code, which is the image of the message space,  consists of codewords of the same length which are closed under addition and scalar multiplication. If the encoded matrix is injective, that is, if no two messages have the same image, or in other words, if the encoding matrix has rank k, then we consider a one to one correspondence between the message space and the linear code. These are the cases that will care, where the encoding is some multiplication by a matrix of rank k, that is, our code is a vector subspace of Fq^n. 

"Domaine(s)" et indice(s) Dewey

• Analyse numérique (518)
• Théorie de l'information (003.54)
• données dans les systèmes informatiques (005.7)
• cryptographie (652.8)
• Mathématiques (510)

Thème(s)