LEADER 05487nam 2200685Ia 450 001 9910465421903321 005 20200520144314.0 010 $a1-299-28125-7 010 $a981-4335-76-2 035 $a(CKB)2560000000099533 035 $a(EBL)1143318 035 $a(OCoLC)830162395 035 $a(SSID)ssj0000832631 035 $a(PQKBManifestationID)12399571 035 $a(PQKBTitleCode)TC0000832631 035 $a(PQKBWorkID)10899300 035 $a(PQKB)11040712 035 $a(MiAaPQ)EBC1143318 035 $a(WSP)00002925 035 $a(Au-PeEL)EBL1143318 035 $a(CaPaEBR)ebr10674380 035 $a(CaONFJC)MIL459375 035 $a(EXLCZ)992560000000099533 100 $a20120928d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAlgebraic geometry modeling in information theory$b[electronic resource] /$fedited by Edgar Martinez Moro 210 $aHackensack, NJ $cWorld Scientific$d2013 215 $a1 online resource (334 p.) 225 0 $aSeries on coding theory and cryptology ;$vv. 8 300 $aDescription based upon print version of record. 311 $a981-4335-75-4 320 $aIncludes bibliographical references. 327 $aContents; Preface; Sage: A Basic Overview for Coding Theory and Cryptography D. Joyner; 0.1. Introduction; 0.2. What is Sage?; 0.2.1. Functionality of selected components of Sage; 0.2.2. History; 0.2.3. Why Python?; 0.2.4. The CLI; 0.2.5. The GUI; 0.2.6. Open source philosophy; 0.3. Coding theory functionality in Sage; 0.3.1. General constructions; 0.3.2. Coding theory functions; 0.3.3. Weight enumerator polynomial; 0.3.4. More code constructions; 0.3.5. Automorphism group of a code; 0.3.6. Even more code constructions; 0.3.7. Block designs and codes; 0.3.8. Special constructions 327 $a0.3.9. Coding theory bounds0.3.10. Asymptotic bounds; 0.4. Cryptography in Sage; 0.4.1. Classical cryptography; 0.4.2. Algebraic cryptosystems; 0.4.3. RSA; 0.4.4. Discrete logs; 0.4.5. Diffle-Hellman; 0.4.6. Linear feedback shift registers; 0.4.7. BBS streamcipher; 0.4.8. Blum-Goldwasser cryptosystem; 0.5. Miscellaneous topics; 0.5.1. Duursma zeta functions; 0.5.2. Self-dual codes; 0.5.3. Cool example (on self-dual codes); 0.6. Coding theory not implemented in Sage; References; Aspects of Random Network Coding O. Geil and C. Thomsen; 1.1. Introduction; 1.2. The network coding problem 327 $a1.2.1. Linear network coding for multicast1.2.2. A polynomial time algorithm for solving the multicast problem; 1.3. Random network coding; 1.3.1. The algebraic approach; 1.3.2. The combinatorial approach; 1.3.2.1. Flow bounds; 1.3.2.2. The bounds by Balli, Yan, and Zhang; 1.4. Bibliographic notes; References; Steganography from a Coding Theory Point of View C. Munuera; 2.1. Introduction; 2.1.1. What is steganography?; 2.1.2. Digital steganography; 2.1.3. Steganography, cryptography and watermarking; 2.1.4. About this chapter; 2.2. Steganographic systems; 2.2.1. The cover 327 $a2.2.2. Steganographic schemes2.2.3. Selection rules; 2.2.4. Parameters; 2.2.5. Proper stegoschemes; 2.3. Error-Correcting codes; 2.3.1. Correcting errors; 2.3.2. Linear codes over fields; 2.3.3. An example: binary Hamming codes; 2.3.4. Generalized Hamming weights for linear codes; 2.4. Linking the problems; 2.4.1. Stegoschemes and error-correcting codes; 2.4.2. Group codes and stegoschemes; 2.4.3. Linear stegoschemes over rings Zq; 2.4.4. Linear stegoschemes over fields; 2.5. Bounds; 2.5.1. The domain of stegoschemes; 2.5.2. Balls and entropy; 2.5.3. A Hamming-like bound 327 $a2.5.4. Asymptotic bounds2.5.5. Perfect stegoschemes; 2.5.6. Another new problem for coding theory; 2.6. Nonshared selection rules; 2.6.1. Wet paper codes; 2.6.2. Solvability and the weight hierarchy of codes; 2.6.3. The rank of random matrices; 2.7. The ZZW embedding construction; 2.7.1. Description of the method; 2.7.2. Asymptotic behavior; 2.8. Bibliographical notes and further reading; Acknowledgments; References; An Introduction to LDPC Codes I. Marquez-Corbella and E. Mart?nez-Moro; 3.1. Introduction; 3.2. Representation for LDPC codes; 3.2.1. Tanner graph; 3.3. Communication channels 327 $a3.4. Decoding algorithms 330 $aAlgebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self 410 0$aSeries on Coding Theory and Cryptology 606 $aCoding theory 606 $aGeometry, Algebraic 606 $aCryptography 608 $aElectronic books. 615 0$aCoding theory. 615 0$aGeometry, Algebraic. 615 0$aCryptography. 676 $a003/.54 701 $aMartinez-Moro$b Edgar$0944377 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465421903321 996 $aAlgebraic geometry modeling in information theory$92131852 997 $aUNINA