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Algebraic testing and weight distributions of codes

M. Kiwi
2003 Theoretical Computer Science  
This framework establishes a connection between testing and the theory of weight distributions of codes.  ...  We illustrate this connection by giving a coding theoretic interpretation of several tests that fall under the label of low-degree tests.  ...  The author gratefully acknowledges the support of Conicyt via Fondecyt No. 1960849, Fundacià on Andes, AT&T via a Ph.D. Scholarship, and NSF via Grant CCR-9503322.  ... 
doi:10.1016/s0304-3975(02)00816-2 fatcat:ofpeondvg5a7fjpgfflnzr2jbm

Page 2244 of Mathematical Reviews Vol. , Issue 87d [page]

1987 Mathematical Reviews  
; Ward, Robert L. 87d:94043 Weight distributions of some irreducible cyclic codes.  ...  Wasan, Siri Krishan (6-DELHI) A note on weak cyclic codes. J. Inform. Optim. Sci. 7 (1986), no. 1, 59-64. Summary: “We determine the weight distribution of each coset of weight one of an (r?  ... 

Page 6322 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
Summary: “Weight distributions of convolutional codes are im- portant because they permit computation of bounds on the error performance.  ...  In this paper, we present a novel approach to com- puting the complete weight distribution function (WDF) of a convolutional code.  ... 

On Integer Programming Problems Related to Soft-Decision Iterative Decoding Algorithms [chapter]

Tadao Kasami
1999 Lecture Notes in Computer Science  
Codes I On the Second Greedy Weight for Binary Linear Codes p. 131 On the Size of Identifying Codes p. 142 Algebra I: Rings and Fields Fast Quantum Fourier Transforms for a Class of Non-abelian  ...  of Block Codes p. 181 Near Optimal Decoding for TCM Using the BIVA and Trellis Shaping p. 191 An Optimality Testing Algorithm for a Decoded Codeword of Binary BlockCodes and Its Computational Complexity  ... 
doi:10.1007/3-540-46796-3_5 fatcat:nsr5gsh23vfsbcrktyoa3zeh3e

Page 8253 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
In the paper under review the author extensively studies weight distributions for algebraic-geometry codes from curves of higher genus.  ...  It is a difficult problem to compute weight distributions for general linear codes. However, it seems possible to do it for algebraic-geometry codes. In 1987, G. L. Katsman and M. A.  ... 

Page 5761 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
(F-TOLN-GN; La Garde) Linear codes with balanced weight distribution. (English summary) Appl. Algebra Engrg. Comm. Comput. 6 (1995), no. 4-5, 299-307.  ...  weight of the code.  ... 

Page 6383 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
We give formal expressions of weight distributions of the cosets of the codes B only depending on m. We can then deduce the weight distributions of the cosets of B.  ...  The weight distributions of the codes are related to the distribution of the number of rational points on the curves.  ... 

Nonadaptive Group Testing With Random Set of Defectives

Arya Mazumdar
2016 IEEE Transactions on Information Theory  
With our relaxed requirements, we show that using explicit constant-weight codes (e.g., based on algebraic geometry codes) we may achieve a number of tests equal to O(t ^2 N/ t) for both the first and  ...  One of the most popular ways of constructing test matrices relies on constant-weight error-correcting codes and their minimum distance.  ...  Acknowledgements: The author would like to thank Alexander Barg for many discussions related to the group testing problem.  ... 
doi:10.1109/tit.2016.2613870 fatcat:dyrxsgz55fehbcukmvgmrrnuua

Page 2958 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
With these two results and classifications of certain types of elements in RM(m, 3) obtained in this paper, the author claims to calculate the previously unknown weight-distribution of the coset xyz+RM  ...  Summary: “Recursive representations of the matrices of two vari- ations of Reed-Muller transforms that are used for first-order Reed-Muller codes and certain Hamming codes are presented, and coding and  ... 

Algebraic manipulation detection codes with perfect nonlinear functions under non-uniform distribution

A.B. Levina, C. Carlet, S.V. Taranov
2017 Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki  
Thus, the weak AMD codes are not tested for the set of errors with zero information part (0 = , , ).  ...  In this work AMD codes based on PN functions were tested for stability, made an overview of changes in the input codeword distribution, irreducible polynomials used to generate code spaces.  ... 
doi:10.17586/2226-1494-2017-17-6-1052-1062 fatcat:x44gdmskjzda7pu5uxuqqpew54

Page 6148 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
(English and French summaries) [Weight distributions of the cosets of binary 2-error-correcting BCH codes] C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 10, 975-980.  ...  Summary: “We prove that, for all even m, there are exactly eight distinct weight distributions for the cosets of the binary 2-error- correcting BCH codes of length n = 2” — 1 or of the extended codes of  ... 

Page 3525 of Mathematical Reviews Vol. , Issue 83h [page]

1983 Mathematical Reviews  
From the introduction: “In the study of the error-correction and error-detection capabilities of a linear code C, it is desirable to determine the weight distribution of each coset of C.  ...  Arakelov (Grozny) Schatz, James R. 83h:94016 On the weight distributions of cosets of a linear code. Amer. Math. Monthly 87 (1980), no. 7, 548-551.  ... 

Chase-type and GMD coset decodings

M.P.C. Fossorier, Shu Lin
2000 IEEE Transactions on Communications  
Consequently, more flexibility in the tradeoffs between error performance and decoding complexity is provided by this generalization, especially for codes with large minimum distance.  ...  of this family.  ...  Kasami for many interesting discussions, and E. Fishler, O. Amrani, and Y. Be'ery for the preprint of their paper [7] .  ... 
doi:10.1109/26.837034 fatcat:34oxaqhmonghzk2woakelfeejq

MLI: An API for Distributed Machine Learning [article]

Evan R. Sparks, Ameet Talwalkar, Virginia Smith, Jey Kottalam, Xinghao Pan, Joseph Gonzalez, Michael J. Franklin, Michael I. Jordan, Tim Kraska
2013 arXiv   pre-print
and highly competitive performance and scalability.  ...  Its primary goal is to simplify the development of high-performance, scalable, distributed algorithms.  ...  to a test class and a training point.  ... 
arXiv:1310.5426v2 fatcat:tzjolo6bubbfvkra5iddgdg4pu

Page 2417 of Mathematical Reviews Vol. , Issue 89D [page]

1989 Mathematical Reviews  
We also determine the full automorphism group and maximum weight of D, and the minimum weight of its dual.” 94B Algebraic theory of error-correcting codes 894:94042 89d:94039 94B05 05C99 Basart, J.  ...  Summary: “We construct a family of linear codes of length N = (")(q—1)"—' and of dimension n (or n—1) over GF(q). Their minimum distance and their weight distribution are calculated.  ... 
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