Information sets of Multiplicity codes
Information sets of Multiplicity codes
We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kop-party. We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions. We also give a complexity estimate of the associated encoding algorithm.
International Symposium on Information Theory, Jun 2015, Hong-Kong, China. IEEE
FOS: Computer and information sciences, Reed-Muller codes, Index Terms—Locally decodable codes, Computer Science - Cryptography and Security, information set, Computer Science - Information Theory, Information Theory (cs.IT), Computational Complexity (cs.CC), Computer Science - Computational Complexity, [INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC], [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], Multiplicity codes, Cryptography and Security (cs.CR), locally correctable codes, [INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR]
FOS: Computer and information sciences, Reed-Muller codes, Index Terms—Locally decodable codes, Computer Science - Cryptography and Security, information set, Computer Science - Information Theory, Information Theory (cs.IT), Computational Complexity (cs.CC), Computer Science - Computational Complexity, [INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC], [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], Multiplicity codes, Cryptography and Security (cs.CR), locally correctable codes, [INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR]
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