Algebraic geometry codes: general theory
暂无分享,去创建一个
[1] Gretchen L. Matthews. Weierstrass Pairs and Minimum Distance of Goppa Codes , 2001, Des. Codes Cryptogr..
[2] Norman E. Hurt. Many Rational Points , 2003 .
[3] Johan P. Hansen,et al. Linkage and Codes on Complete Intersections , 2003, Applicable Algebra in Engineering, Communication and Computing.
[4] Juergen Bierbrauer. Introduction to coding theory , 2005, Discrete mathematics and its applications.
[5] H. Niederreiter,et al. Rational Points on Curves Over Finite Fields: Theory and Applications , 2001 .
[6] R. Schoof,et al. Weight formulas for ternary Melas codes , 1992 .
[7] Peter Beelen,et al. A generalization of the Weierstrass semigroup , 2006 .
[8] K. Lauter. Deligne–Lusztig curves as ray class fields , 1999 .
[9] V. D. Goppa. Codes on Algebraic Curves , 1981 .
[10] Peter Beelen,et al. Asymptotically good towers and differential equations , 2004, Compositio Mathematica.
[11] J. H. Lint,et al. Introduction to coding theory and algebraic geometry , 1989 .
[12] Iwan M. Duursma,et al. Decoding codes from curves and cyclic codes , 1993 .
[13] Harvey Cohn,et al. Introduction to the construction of class fields , 1985 .
[14] John Talbot,et al. The number of points on an algebraic curve over a finite field , 2007 .
[15] Iwan M. Duursma,et al. Reed-Muller Codes on Complete Intersections , 2001, Applicable Algebra in Engineering, Communication and Computing.
[16] Iwan M. Duursma,et al. Weight distributions of geometric Goppa codes , 1999 .
[17] N. Elkies. Explicit Towers of Drinfeld Modular Curves , 2000, math/0005140.
[18] Chaoping Xing,et al. Nonlinear codes from algebraic curves improving the Tsfasman-Vladut-Zink bound , 2003, IEEE Transactions on Information Theory.
[19] M. Tsfasman,et al. Algebraic Geometric Codes: Basic Notions , 2007 .
[20] Masaaki Homma,et al. The Complete Determination of the Minimum Distance of Two-Point Codes on a Hermitian Curve , 2006, Des. Codes Cryptogr..
[21] Cícero Carvalho,et al. On Goppa Codes and Weierstrass Gaps at Several Points , 2005, Des. Codes Cryptogr..
[22] Alexander Vardy,et al. Correcting errors beyond the Guruswami-Sudan radius in polynomial time , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).
[23] Michael A. Tsfasman,et al. Geometric approach to higher weights , 1995, IEEE Trans. Inf. Theory.
[24] F. Torres,et al. Algebraic Curves over Finite Fields , 1991 .
[25] Richard E. Blahut. Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach , 2008 .
[26] M. Tsfasman,et al. Modular curves, Shimura curves, and Goppa codes, better than Varshamov‐Gilbert bound , 1982 .
[27] Iwan M. Duursma,et al. A symmetric Roos bound for linear codes , 2006, J. Comb. Theory, Ser. A.
[28] Dirk Ehrhard,et al. Achieving the designed error capacity in decoding algebraic-geometric codes , 1993, IEEE Trans. Inf. Theory.
[29] N. Hurt,et al. Many Rational Points: Coding Theory and Algebraic Geometry , 2003 .
[30] Jens Peter Pedersen,et al. Automorphism groups of Ree type Deligne-Lusztig curves and function fields. , 1993 .
[31] Gretchen L. Matthews. Codes from the Suzuki function field , 2004, IEEE Transactions on Information Theory.
[32] Iwan M. Duursma,et al. Monomial embeddings of the Klein curve , 1999, Discret. Math..
[33] W. Cary Huffman,et al. Fundamentals of Error-Correcting Codes , 1975 .
[34] O. Antoine,et al. Theory of Error-correcting Codes , 2022 .
[35] Seung Kook Park. Applications of Algebraic Curves to Cryptography , 2007 .
[36] H. Stichtenoth,et al. A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound , 1995 .
[37] Yuan Zhou. Introduction to Coding Theory , 2010 .
[38] T. R. N. Rao,et al. Decoding algebraic-geometric codes up to the designed minimum distance , 1993, IEEE Trans. Inf. Theory.
[39] Kenneth W. Shum,et al. A low-complexity algorithm for the construction of algebraic-geometric codes better than the Gilbert-Varshamov bound , 2001, IEEE Trans. Inf. Theory.
[40] V. D. Goppa. Geometry and Codes , 1988 .
[41] Henning Stichtenoth,et al. Algebraic function fields and codes , 1993, Universitext.
[42] J. H. van Lint,et al. Introduction to Coding Theory , 1982 .
[43] Gábor Korchmáros,et al. Quotient curves of the Suzuki curve , 2006 .
[44] Serguei A. Stepanov,et al. Codes on Algebraic Curves , 1999 .
[45] Peter Beelen,et al. The order bound for general algebraic geometric codes , 2007, Finite Fields Their Appl..
[46] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[47] Harald Niederreiter,et al. Low-discrepancy sequences obtained from algebraic function fields over finite fields , 1995 .
[48] Iwan M. Duursma,et al. Geometric Reed-Solomon codes of length 64 and 65 over F8 , 2003, IEEE Trans. Inf. Theory.
[49] R. Schoof. Families of curves and weight distributions of codes , 1995, math/9504222.
[50] Cem Güneri. Algebraic geometric codes: basic notions , 2008 .
[51] Iwan M. Duursma. Algebraic decoding using special divisors , 1993, IEEE Trans. Inf. Theory.
[52] Iwan M. Duursma,et al. Majority coset decoding , 1993, IEEE Trans. Inf. Theory.
[53] Chaoping Xing,et al. Excellent nonlinear codes from algebraic function fields , 2005, IEEE Transactions on Information Theory.
[54] Tom Høholdt,et al. An explicit construction of a sequence of codes attaining the Tsfasman-Vladut-Zink bound: The first steps , 1997, IEEE Trans. Inf. Theory.
[55] Seon Jeong Kim. On the index of the Weierstrass semigroup of a pair of points on a curve , 1994 .
[56] Iwan M. Duursma,et al. Preparata codes through lattices , 2001, IEEE Trans. Inf. Theory.
[57] Noam D. Elkies,et al. Explicit Modular Towers , 2001, math/0103107.
[58] Hao Chen,et al. Algebraic Geometric Secret Sharing Schemes and Secure Multi-Party Computations over Small Fields , 2006, CRYPTO.
[59] Venkatesan Guruswami,et al. Correlated Algebraic-Geometric Codes: Improved List Decoding over Bounded Alphabets , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).
[60] Johan P. Hansen,et al. Algebraic Geometry Codes , 2005 .
[61] Henning Stichtenoth,et al. Group codes on certain algebraic curves with many rational points , 1990, Applicable Algebra in Engineering, Communication and Computing.
[62] S. G. Vladut,et al. Algebraic-Geometric Codes , 1991 .
[63] Dirk Ehrhard,et al. Decoding Algebraic-Geometric Codes by solving a key equation , 1992 .
[64] Venkatesan Guruswami,et al. Improved decoding of Reed-Solomon and algebraic-geometry codes , 1999, IEEE Trans. Inf. Theory.
[65] Oliver Pretzel,et al. Codes and Algebraic Curves , 1998 .
[66] H. Stichtenoth,et al. EXPLICIT TOWERS OF FUNCTION FIELDS OVER FINITE FIELDS , 2006 .
[67] Ruud Pellikaan,et al. The minimum distance of codes in an array coming from telescopic semigroups , 1995, IEEE Trans. Inf. Theory.
[68] Judy L. Walker,et al. Codes and Curves , 2000, Student mathematical library.
[69] Aart Blokhuis,et al. Hermitian unitals are code words , 1991, Discret. Math..
[70] Noam D. Elkies,et al. Excellent codes from modular curves , 2001, STOC '01.
[71] Jens Peter Pedersen,et al. A function field related to the Ree group , 1992 .
[72] P. V. Kumar,et al. On the true minimum distance of Hermitian codes , 1992 .
[73] Jason McCullough,et al. A GENERALIZED FLOOR BOUND FOR THE MINIMUM DISTANCE OF GEOMETRIC GOPPA CODES AND ITS APPLICATION TO TWO-POINT CODES , 2004, math/0408341.
[74] Chen Hao. Algebraic geometric codes with applications , 2007 .
[75] R. F. Lax,et al. Consecutive Weierstrass gaps and minimum distance of Goppa codes , 1993 .
[76] Gretchen L. Matthews,et al. On the floor and the ceiling of a divisor , 2006, Finite Fields Their Appl..
[77] Jennifer D. Key. Hermitian varieties as codewords , 1991, Des. Codes Cryptogr..