메뉴 건너뛰기




Volumn 38, Issue 5, 2008, Pages 1952-1969

Locally decodable codes from nice subsets of finite fields and prime factors of Mersenne numbers

Author keywords

Locally decodable codes; Mersenne primes

Indexed keywords

CODEWORD; FINITE FIELDS; LOCALLY-DECODABLE CODES; MERSENNE PRIMES; PRIME FACTORS; QUERY COMPLEXITY; UPPER BOUND;

EID: 78751546228     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/070696519     Document Type: Article
Times cited : (13)

References (39)
  • 3
    • 21144453606 scopus 로고    scopus 로고
    • General constructions for information-theoretic private information retrieval
    • DOI 10.1016/j.jcss.2005.03.002, PII S0022000005000309
    • A. Beimel, Y. Ishai, and E. Kushilevitz, General constructions for information-theoretic private information retrieval, J. Comput. System Sci., 71 (2005), pp. 213-247. (Pubitemid 40878949)
    • (2005) Journal of Computer and System Sciences , vol.71 , Issue.2 , pp. 213-247
    • Beimel, A.1    Ishai, Y.2    Kushilevitz, E.3
  • 5
    • 33646051576 scopus 로고    scopus 로고
    • A Gauss sum estimate in arbitrary finite fields
    • DOI 10.1016/j.crma.2006.01.022, PII S1631073X06000501
    • J. Bourgain and M. Chang, A Gauss sum estimate in arbitrary finite fields, C. R. Math. Acad. Sci. Paris, 342 (2006), pp. 643-646. (Pubitemid 43607961)
    • (2006) Comptes Rendus Mathematique , vol.342 , Issue.9 , pp. 643-646
    • Bourgain, J.1    Chang, M.-C.2
  • 9
    • 84941430071 scopus 로고
    • Die Nullstellen der Kongruenz Zetafunktion in gewissen zyklischen Fallen
    • H. Davenport and H. Hasse, Die Nullstellen der Kongruenz Zetafunktion in gewissen zyklischen Fallen, J. Reine Angew. Math., 172 (1935), pp. 151-182.
    • (1935) J. Reine Angew. Math. , vol.172 , pp. 151-182
    • Davenport, H.1    Hasse, H.2
  • 11
    • 0042347567 scopus 로고
    • p - 1 for a prime p and other expressions
    • p - 1 for a prime p and other expressions, Acta. Arith., 30 (1976), pp. 257-265.
    • (1976) Acta. Arith. , vol.30 , pp. 257-265
    • Erdos, P.1    Shorey, T.2
  • 19
    • 4544225791 scopus 로고    scopus 로고
    • Exponential lower bound for 2-query locally decodable codes via a quantum argument
    • I. Kerenidis and R. de Wolf, Exponential lower bound for 2-query locally decodable codes via a quantum argument, J. Comput. System Sci., 69 (2004), pp. 395-420.
    • (2004) J. Comput. System Sci. , vol.69 , pp. 395-420
    • Kerenidis, I.1    De Wolf, R.2
  • 20
    • 0004127220 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, UK, 1983.
    • (1983) Finite Fields
    • Lidl, R.1    Niederreiter, H.2
  • 22
    • 77957231111 scopus 로고    scopus 로고
    • On the largest prime factor of a Mersenne number
    • AMS, Providence, RI
    • L. Murata and C. Pomerance, On the largest prime factor of a Mersenne number, inNumber Theory, CRM Proc. Lecture Notes 36, AMS, Providence, RI, 2004, pp. 209-218.
    • (2004) Number Theory, CRM Proc. Lecture Notes , vol.36 , pp. 209-218
    • Murata, L.1    Pomerance, C.2
  • 24
    • 84959056761 scopus 로고    scopus 로고
    • Optimal lower bounds for 2-query locally decodable linear codes
    • Randomization and Approximation Techniques in Computer Science, Springer-Verlag, Berlin
    • K. Obata, Optimal lower bounds for 2-query locally decodable linear codes, in Randomization and Approximation Techniques in Computer Science, Lecture Notes in Comput. Sci. 2483, Springer-Verlag, Berlin, 2002, pp. 39-50.
    • (2002) Lecture Notes in Comput. Sci. , vol.2483 , pp. 39-50
    • Obata, K.1
  • 26
    • 0040019849 scopus 로고
    • Recent developments in primality testing
    • C. Pomerance, Recent developments in primality testing, Math. Intelligencer, 3 (1980/81), pp. 97-105.
    • (1980) Math. Intelligencer , vol.3 , pp. 97-105
    • Pomerance, C.1
  • 31
    • 0000283497 scopus 로고
    • On divisors of Fermat, Fibonacci, Lucas, and Lehmer numbers
    • C. Stewart, On divisors of Fermat, Fibonacci, Lucas, and Lehmer numbers, Proc. London Math. Soc. (3), 35 (1977), pp. 425-447.
    • (1977) Proc. London Math. Soc. , vol.35 , Issue.3 , pp. 425-447
    • Stewart, C.1
  • 33
    • 33748588052 scopus 로고    scopus 로고
    • Some applications of coding theory in computational complexity
    • Department of Mathematics, Seconda Univ. Napoli, Caserta, Italy
    • L. Trevisan, Some applications of coding theory in computational complexity, in Complexity of Computations and Proofs, Quad. Mat. 13, Department of Mathematics, Seconda Univ. Napoli, Caserta, Italy, 2004, pp. 347-424.
    • (2004) Complexity of Computations and Proofs, Quad. Mat. , vol.13 , pp. 347-424
    • Trevisan, L.1
  • 34
    • 84966232699 scopus 로고
    • Divisors of Mersenne numbers
    • S. Wagstaff, Divisors of Mersenne numbers, Math. Comp., 40 (1983), pp. 385-397.
    • (1983) Math. Comp. , vol.40 , pp. 385-397
    • Wagstaff, S.1
  • 35
    • 26444620133 scopus 로고    scopus 로고
    • Improved lower bounds for locally decodable codes and private information retrieval
    • Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP'05), Springer-Verlag, Berlin
    • S. Wehner and R. de Wolf, Improved lower bounds for locally decodable codes and private information retrieval, in Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP'05), Lecture Notes in Comput. Sci. 3580, Springer- Verlag, Berlin, pp. 1424-1436.
    • Lecture Notes in Comput. Sci. , vol.3580 , pp. 1424-1436
    • Wehner, S.1    De Wolf, R.2
  • 36
    • 51849119700 scopus 로고    scopus 로고
    • Corruption and recovery-efficient locally decodable codes
    • D. Woodruff, Corruption and recovery-efficient locally decodable codes, in Proceedings of the 12th RANDOM, 2008, pp. 584-595.
    • (2008) Proceedings of the 12th RANDOM , pp. 584-595
    • Woodruff, D.1
  • 38
    • 40549114927 scopus 로고    scopus 로고
    • Towards 3-query locally decodable codes of subexponential length
    • S. Yekhanin, Towards 3-query locally decodable codes of subexponential length, J. ACM, 55 (2008), pp. 1-14.
    • (2008) J. ACM , vol.55 , pp. 1-14
    • Yekhanin, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.