Filters








1,668 Hits in 3.9 sec

Linear Codes Of 2-Designs As Subcodes Of The Extended Generalized Reed-Muller Codes [article]

Zhiwen He, Jiejing Wen
2020 arXiv   pre-print
The linear codes generated by the rows of these incidence matrix are subcodes of the extended codes of the 4-th order generalized Reed-Muller codes and they also hold 2-designs.  ...  We compute the incidence matrices of 2-designs that are supported by the minimum weight codewords of these ternary codes.  ...  Acknowledgement The work of the first author was supported by National Natural Science Foundation of China under Grant No. 11771392.  ... 
arXiv:2007.14106v1 fatcat:3fzylwhhvvagjk7bkjju4ivo2u

Weight enumeration of codes from finite spaces

Relinde P. M. J. Jurrius
2011 Designs, Codes and Cryptography  
As a result from the geometric method we use for the weight enumeration, we also completely determine the set of supports of subcodes and words in an extension code.  ...  We study the generalized and extended weight enumerator of the q-ary Simplex code and the q-ary first order Reed-Muller code.  ...  Acknowledgments The author would like to thank Vladimir Tonchev for coming up with the question about the weight enumerator of the extension codes of the Simplex code, and for his encouraging conversations  ... 
doi:10.1007/s10623-011-9557-2 fatcat:hmihrf6q4bfbjnaf6ykgsb26pu

Stanley–Reisner resolution of constant weight linear codes

Trygve Johnsen, Hugues Verdure
2012 Designs, Codes and Cryptography  
Given a constant weight linear code, we investigate its weight hierarchy and the Stanley-Reisner resolution of its associated matroid regarded as a simplicial complex.  ...  We also exhibit conditions on the higher weights sufficient to conclude that the code is of constant weight  ...  Translated to coding theory, a Grassmannian is a space that parametrizes all the linear subcodes of a given dimension of a linear code.  ... 
doi:10.1007/s10623-012-9767-2 fatcat:s5hm2ejdwbdupb54nmfye7soya

Support Weight Enumerators and Coset Weight Distributions of Isodual Codes

Olgica Milenkovic
2005 Designs, Codes and Cryptography  
In this paper various methods for computing the support weight enumerators of binary, linear, even, isodual codes are described.  ...  from the other.  ...  The r-th generalized Hamming weight of a linear code C, d r (C), is the minimum support weight of any subcode of C that has dimension r.  ... 
doi:10.1007/s10623-003-6152-1 fatcat:yosxihgjxvh6hifhdpcmndlbny

Optimum Linear Codes with Support Constraints over Small Fields [article]

Hikmet Yildiz, Babak Hassibi
2018 arXiv   pre-print
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix.  ...  We show that the largest minimum distance can be achieved by a subcode of a Reed-Solomon code of small field size.  ...  INTRODUCTION The problem of designing a linear code with the largest possible minimum distance, subject to support constraints on the generator matrix, has recently found several applications.  ... 
arXiv:1803.03752v1 fatcat:f3xn6emvuzcqjjnep7qqhxpl54

Code constructions and existence bounds for relative generalized Hamming weight

Zhuojun Zhuang, Yuan Luo, Bin Dai
2012 Designs, Codes and Cryptography  
The relative generalized Hamming weight (RGHW) of a linear code C and a subcode C 1 is an extension of generalized Hamming weight.  ...  The concept was firstly used to protect messages from an adversary in the wiretap channel of type II with illegitimate parties.  ...  This work is supported in part by the National Key  ... 
doi:10.1007/s10623-012-9657-7 fatcat:4hsu3lhjpjdt5ias3vigy43ydy

Optimal Locally Repairable Codes for Parallel Reading

Jie Hao, Kenneth W. Shum, Shu-Tao Xia, Deyin Li
2020 IEEE Access  
Moreover, multiple repair subcodes can support parallel readings of data, thus make the proposed codes attractive for distributed storage systems with hot data.  ...  distance δ, and the i-th information symbol is the unique common code symbol of these t subcodes, furthermore, each subcode contains exactly δ − 1 parity symbols.  ...  One important class of such matrices are incidence matrices of certain objects from combinatorial designs, e.g., generalized quadrangle, 2-design, or projective plane, etc [26] .  ... 
doi:10.1109/access.2020.2992188 fatcat:cwhtiowc3vevfmrjsljgozmh7a

Steiner systems S(2, 4, 3^m-1/2) and 2-designs from ternary linear codes of length 3^m-1/2 [article]

Chunming Tang, Cunsheng Ding, Maosheng Xiong
2019 arXiv   pre-print
This paper mainly confirms some recent conjectures of Ding and Li regarding Steiner systems and 2-designs from a special type of ternary projective codes.  ...  Coding theory and t-designs have close connections and interesting interplay. In this paper, we first introduce a class of ternary linear codes and study their parameters.  ...  In addition, we construct more 2-designs from subcodes of C 0, 1, . . . , ⌊ m 2 ⌋ . Let C be an [n, k, d] linear code.  ... 
arXiv:1901.09228v2 fatcat:hgp2pq4shfc4hghaqzwqoz3dqu

On The Dimension of The Subfield Subcodes of 1-Point Hermitian Codes [article]

Sabira El Khalfaoui, Gábor P. Nagy
2019 arXiv   pre-print
In this paper we present new values of the true dimension of subfield subcodes of 1–point Hermitian codes, including the case when the subfield is not binary.  ...  Subfield subcodes of algebraic-geometric codes are good candidates for the use in post-quantum cryptosystems, provided their true parameters such as dimension and minimum distance can be determined.  ...  Hence, an essential ingredient of their schemes is a binary linear code C which has an efficient decoding algorithm and which cannot be distinguished from the random linear code.  ... 
arXiv:1906.10444v2 fatcat:cff2msqwpvbsbfrpntc62g6jrm

On the dimension of the subfield subcodes of 1-point Hermitian codes

Sabira El Khalfaoui, ,Bolyai Institute of the University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary, Gábor P. Nagy, ,Department of Algebra of the Budapest University of Technology and Economics, Egry József utca 1, H-1111 Budapest, Hungary
2019 Advances in Mathematics of Communications  
In this paper we present new values of the true dimension of subfield subcodes of 1-point Hermitian codes, including the case when the subfield is not binary.  ...  Subfield subcodes of algebraic-geometric codes are good candidates for the use in post-quantum cryptosystems, provided their true parameters such as dimension and minimum distance can be determined.  ...  Hence, an essential ingredient of their schemes is a binary linear code C which has an efficient decoding algorithm and which cannot be distinguished from the random linear code.  ... 
doi:10.3934/amc.2020054 fatcat:5fjrjcwqfjebxanlquizqam3oy

Full-diversity product codes for block erasure and block fading channels

Joseph J. Boutros, Gilles Zemor, Albert Guillen i Fabregas, Ezio Biglieri
2008 2008 IEEE Information Theory Workshop  
The concept of a rootcheck or a root subcode is introduced by generalizing the same principle recently invented for low-density parity-check codes.  ...  We also describe some channel related graphical properties of the new family of product codes, a family referred to as root product codes. 978-1-4244-2270-8/08/$25.00 ©2008 IEEE  ...  In our practical examples, we mainly focus on subcodes defined from the famous family of linear binary BCH codes [4] [13] .  ... 
doi:10.1109/itw.2008.4578676 dblp:conf/itw/BoutrosZFB08 fatcat:wrd4xlkryrgmpjk2bhspuotjee

Bent Vectorial Functions, Codes and Designs [article]

Cunsheng Ding, Akihiro Munemasa, Vladimir Tonchev
2019 arXiv   pre-print
The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem,  ...  A new coding-theoretic characterization of bent vectorial functions is presented.  ...  The research of Cunsheng Ding was supported by the Hong Kong Research Grants Council, under Grant No. 16300418.  ... 
arXiv:1808.08487v2 fatcat:65gykj4dlngejpms3gvgymtite

Greedy weights for matroids

Trygve Johnsen, Hugues Verdure
2020 Designs, Codes and Cryptography  
Thus our Wei duality is a generalization of that for linear codes given by Schaathun.  ...  AbstractWe introduce greedy weights of matroids, inspired by those for linear codes. We show that a Wei duality holds for two of these types of greedy weights for matroids.  ...  From [17, Theorem 2.2.8] , the matroid associated to the dual of linear code is precisely the dual of the matroid of the linear code in question Greedy weights and resolutions of Stanley-Reisner rings  ... 
doi:10.1007/s10623-020-00824-w fatcat:frgbomwbnfclzaqqyxljdb2iqe

Foreword: Computer Algebra in Coding Theory and Cryptography

I. Kotsireas, Edgar Martínez-Moro
2015 Designs, Codes and Cryptography  
The paper Quantum codes from affine variety codes and their subfield-subcodes, by C. Galindo and F.  ...  Hernando, presents and analyzes a construction of quantum stabilizer codes from affine variety codes and their subfield-subcodes. 3. Cryptography. In Hamming codes for wet paper steganography, by C.  ... 
doi:10.1007/s10623-015-0041-2 fatcat:qfoajsxgb5eopdn56wdj5jzaei

The Second Support Weight Distribution of the Kasami Codes

H.G. Schaathun, T. Helleseth
2005 IEEE Transactions on Information Theory  
We compute the second support weight distribution of the Kasami codes. Index Terms-Kasami code, support weight distribution.  ...  INTRODUCTION The support weight distribution (SWD) of linear codes was introduced by Helleseth, Kløve, and Mykkeltveit [1] .  ...  From the SWD of a single code, they were able to determine the weight distribution of a corresponding infinite class of codes.  ... 
doi:10.1109/tit.2005.851770 fatcat:lt3pevv6sjgkbe4npgcogpgy7q
« Previous Showing results 1 — 15 out of 1,668 results