Results 1 - 10 of 85

The Z_4-linearity of Kerdock, Preparata, Goethals, and related codes

by A. Roger Hammons, Jr., P. Vijay Kumar, A. R. Calderbank, N. J. A. Sloane, Patrick Solé , 2001
"... Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals. It is shown here that all these codes can be very simply constructed as binary images under the ..."
Abstract - Cited by 178 (15 self) - Add to MetaCart
are extended cyclic codes over ¡ 4, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the ‘Preparata ’ code and a Hadamard-transform soft-decision decoding algorithm for the Kerdock code. Binary first- and second-order Reed-Muller codes are also linear

Algebraic Constructions of Nonbinary Quasi-Cyclic LDPC Codes: Array Masking and Dispersion ∗

by Shu Lin, Shumei Song, Bo Zhou, Jingyu Kang, Ying Y. Tai, Qin Huang
"... Abstract — This paper is concerned with algebraic constructions of nonbinary quasi-cyclic (QC) LDPC codes based on arrays of circulant permutation matrices constructed from finite fields. Two methods, array masking and dispersion, are presented for constructing nonbinary QC-LDPC codes. Simulation re ..."
Abstract - Cited by 11 (1 self) - Add to MetaCart
results show that codes constructed by these methods perform very well with iterative decoding based on belief propagation. They achieve significant coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision decoding or algebraic soft-decision decoding

Some Algebraic and Geometric Computations in PSPACE

by John Canny , 1988
"... We give a PSPACE algorithm for determining the signs of multivariate polynomials at the common zeros of a sys-tem of polynomial equations. One of the consequences of this result is that the “Generalized Movers ’ Problem ” in robotics drops from EXPTIME into PSPACE, and is there-fore PSPACE-complete ..."
Abstract - Cited by 168 (2 self) - Add to MetaCart
combines t1.e tl;eorem of the primitive element from classical algebra with a sym-bolic polynomial evaluation lemma from [BKR]. A decision problem involving several algrtbraic IIUIII~W~S is rctl~~c-~d to a problem involving a siuglc illgel)rilic u~tt~ber or pritnit.ive clement, which rationally grueratrs

On Generalized Minimum Distance Decoding Thresholds for the AWGN Channel

by Christian Senger, Vladimir R. Sidorenko, Victor V. Zyablov , 903
"... Abstract — We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block code to exploit soft information obtained from the demodulator. This idea goes back to Forne ..."
Abstract - Cited by 3 (3 self) - Add to MetaCart
Abstract — We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block code to exploit soft information obtained from the demodulator. This idea goes back

The Z_4-Linearity of Kerdcck, Preparata, Goethals, and Related Codes

by A. Roger Hammons, Jr., P. Vijay Kumar, A. R. Calderbank, N. J. A. Sloane, Patrick Sole , 1994
"... Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals. It is shown here that all these codes can be very simply constructed as binary images under the ..."
Abstract - Add to MetaCart
are extended cyclic codes over Z4, which greatly simplies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the “Preparata” code and a Hadamard-transform softdecision decoding algorithm for the Kerdock code. Binary firstand second-order Reed-Muller codes are also linear over

Hardness of decision (R)LWE for any modulus

by Adeline Langlois, Damien Stehlé , 2012
"... Abstract. The decision Learning With Errors problem has proven an extremely flexible foundation for devising provably secure cryptographic primitives. LWE can be expressed in terms of linear algebra over Z/qZ. This modulus q is the subject of study of the present work. When q is prime and small, or ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
Abstract. The decision Learning With Errors problem has proven an extremely flexible foundation for devising provably secure cryptographic primitives. LWE can be expressed in terms of linear algebra over Z/qZ. This modulus q is the subject of study of the present work. When q is prime and small

Efficient Interpolation and Factorization in Algebraic Soft-Decision Decoding of Reed-Solomon Codes

by Ralf Koetter, Jun Ma, Alexander Vardy, Arshad Ahmed , 2003
"... Algebraic soft-decision decoding of Reed-Solomon codes delivers promising coding gains over conventional hard-decision decoding. The main computational steps in algebraic soft-decoding (as well as Sudan-type list-decoding) are bivariate interpolation and factorization. We discuss a new computational ..."
Abstract - Cited by 15 (9 self) - Add to MetaCart
Algebraic soft-decision decoding of Reed-Solomon codes delivers promising coding gains over conventional hard-decision decoding. The main computational steps in algebraic soft-decoding (as well as Sudan-type list-decoding) are bivariate interpolation and factorization. We discuss a new

Hardware Complexities of Algebraic Soft-decision Reed-Solomon Decoders and Comparisons

by Xinmiao Zhang, Jiangli Zhu
"... Abstract—Algebraic soft-decision (ASD) decoding of Reed-Solomon (RS) codes can achieve significant coding gain over hard-decision decoding. For practical implementation purpose, ASD algorithms with simple multiplicity assignment schemes are preferred. This paper answers the question of which practic ..."
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Abstract—Algebraic soft-decision (ASD) decoding of Reed-Solomon (RS) codes can achieve significant coding gain over hard-decision decoding. For practical implementation purpose, ASD algorithms with simple multiplicity assignment schemes are preferred. This paper answers the question of which

Anonymous Hierarchical Identity-Based Encryption (Without Random Oracles). In: Dwork

by Xavier Boyen , Brent Waters - CRYPTO 2006. LNCS, , 2006
"... Abstract We present an identity-based cryptosystem that features fully anonymous ciphertexts and hierarchical key delegation. We give a proof of security in the standard model, based on the mild Decision Linear complexity assumption in bilinear groups. The system is efficient and practical, with sm ..."
Abstract - Cited by 119 (10 self) - Add to MetaCart
was first used by Joux Decision Linear: The Linear assumption was first proposed by Boneh, Boyen, and Shacham for group signatures "Hard" means algorithmically non-solvable with probability 1 /2 + Ω(poly(Σ) −1 ) in time O(poly(Σ)) for efficiently generated random "bilinear instances

Performance analysis of algebraic soft-decision decoding of reed-solomon codes

by Andrew Duggan, Er Barg - in Proc. Allerton , 2006
"... Abstract — We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. An expression is derived for the error correction radius within which the softdecision decoder produces a list that contains the transmitt ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
the transmitted codeword. The error radius for ASD is shown to be larger than that of Guruswami-Sudan (GS) hard-decision decoding for a subset of low-rate codes. These results are also extended to multivariable interpolation in the sense of Parvaresh and Vardy. An upper bound is then presented for ASD’s
Results 1 - 10 of 85