Notice
1.3. Encoding (Linear Transformation)
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Descriptif
In this session, we willtalk about the easy map of the - one-way trapdoor functionsbased on error-correcting codes. We suppose that the set of all messages that we wish to transmit is the set of k-tuples havingelements from the field Fq. There are qk possiblemessages and we referred to it as the message space. In order to detect andpossibly correct errors, we add some redundancy, thus the ktuples will be embedded into n-tuples with n greater than k. In this MOOC, we will focus on linearencoder that is linear transformations. Every linear transformation can berepresented by a matrix multiplication. Thus our code, which is theimage of the message space, consists of codewords of thesame length which are closed under addition andscalar multiplication. If the encoded matrixis injective, that is, if no two messages have thesame image, or in other words, if the encoding matrix hasrank k, then we consider a one to one correspondence between themessage space and the linear code. These are the cases thatwill care, where the encoding is some multiplication by amatrix of rank k, that is, our code is a vector subspace of Fq^n.
Intervention
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