Search Results - linear binary code

New Upper Bounds on Binary Linear Codes and a -Code With a Better-Than-Linear Gray Image by Kiermaier, Michael, Wassermann, Alfred, Zwanzger, Johannes

“…Using integer linear programming and table-lookups, we prove that there is no binary linear [1988, 12, 992] code…”
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New [52, 18, 16] Linear Binary Block Code by Fizel, Peter, Farkaš, Peter

“…The generator matrix and the weight distribution of a new [52, 18, 16] linear binary block code are presented…”
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Construction of minimal binary linear codes with dimension n+3 by Shaikh, Wajid M., Jain, Rupali S., Reddy, B. Surendranath, Patil, Bhagyashri S.

“…In this paper, for n ≥ 6 , we present the generic construction of binary linear codes of length 2 n - 1 with dimension n…”
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Some Punctured Codes of Several Families of Binary Linear Codes by Wang, Xiaoqiang, Zheng, Dabin, Ding, Cunsheng

“…Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature…”
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Minimal Binary Linear Codes by Ding, Cunsheng, Heng, Ziling, Zhou, Zhengchun

“… Minimal linear codes, a special type of linear codes, are preferred in secret sharing. In this paper, a necessary and sufficient condition for a binary linear code to be minimal is derived…”
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New [47,15,16] Linear Binary Block Code by Janosov, M., Husak, M., Farkas, P., Armada, A.G.

“…A new [47,15,16] linear binary block code and its weight spectrum is presented. The code is better than the previously known [47,15,16…”
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Wide minimal binary linear codes from the general Maiorana–McFarland class by Zhang, Fengrong, Pasalic, Enes, Rodríguez, René, Wei, Yongzhuang

“… . In this article, we extend the initiative originally taken by Ding et al. in [ 8 ] to design minimal binary linear codes that satisfy w min / w max…”
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At most three-weight binary linear codes from generalized Moisio’s exponential sums by Wu, Yansheng, Yue, Qin, Shi, Xueying

“…:644–651, 2009 ). As applications, we present two classes of binary linear codes with two wights or three weights…”
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Four classes of minimal binary linear codes with wmin/wmax<1/2 derived from Boolean functions by Li, Xia, Yue, Qin

“… This paper gives the weight distributions of four classes of minimal binary linear codes with w min / w max…”
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Four classes of minimal binary linear codes with$$w_{min}/w_{max}<1/2$$derived from Boolean functions by Li, Xia, Yue, Qin

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All Binary Linear Codes That Are Invariant Under }2(n) by Ding, Cunsheng, Liu, Hao, Tonchev, Vladimir D.

“…The projective special linear group <inline-formula> <tex-math notation="LaTeX">{\mathrm {PSL}}_{2}(n) </tex-math></inline-formula> is 2-transitive for all primes…”
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Using linear programming to Decode Binary linear codes by Feldman, J., Wainwright, M.J., Karger, D.R.

“…A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel…”
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Entanglement-assisted quantum codes from arbitrary binary linear codes by Qian, Jianfa, Zhang, Lina

“… ] ] EAQEC codes from arbitrary binary [ n , k , d ] linear codes, where the parameter of ebits c…”
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Optimal Binary Linear Codes From Maximal Arcs by Heng, Ziling, Ding, Cunsheng, Wang, Weiqiong

“… The first objective of this paper is to construct a class of binary linear codes with parameters <inline-formula> <tex-math notation="LaTeX">[{2^{m+s}+2^{s}-2^{m},2^{m+s}+2^{s}-2^{m}-2m-2,4}] </tex-math></inline-formula…”
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Adaptive Cut Generation Algorithm for Improved Linear Programming Decoding of Binary Linear Codes by Xiaojie Zhang, Siegel, P. H.

“…Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP…”
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Binary Linear Codes With Three Weights by Ding, Kelan, Ding, Cunsheng

“…In this paper, a class of binary three-weight linear codes is constructed. Their dual codes are also studied…”
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Optimal minimal linear codes from posets by Hyun, Jong Yoon, Kim, Hyun Kwang, Wu, Yansheng, Yue, Qin

“…Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al…”
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A construction of binary linear codes from Boolean functions by Ding, Cunsheng

“… Two generic constructions of binary linear codes with Boolean functions have been well investigated in the literature…”
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Binary linear codes and binary matrices by Harz Allah, Idris

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Binary Linear Codes With Optimal Scaling: Polar Codes With Large Kernels by Fazeli, Arman, Hassani, Hamed, Mondelli, Marco, Vardy, Alexander

“… under the best possible scaling of their block length as a function of the gap to capacity. This result exhibits the first known family of binary codes that attain both optimal scaling and quasi-linear complexity of encoding and decoding…”
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