Search Results - Optimal binary linear code

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"> [2ᵐ⁺ˢ+2ˢ-2ᵐ,2ᵐ⁺ˢ+2ˢ-2ᵐ-2m-2,4]</tex-math></inline-formula…”
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On the Error Coefficients of Asymptotic Frame Error Rate Optimal Binary Linear Codes by Li, Shitao, Luo, Gaojun, Shi, Minjia, Ling, San

“…A binary linear code is called asymptotic frame error rate (AFER)-optimal if it achieves the maximum possible value of the minimum distance while having the smallest value of the corresponding error coefficient…”
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Infinite Families of Few Weight Optimal Binary Linear Codes From Multivariable Functions by Yoon Hyun, Jong, Jeong, Jihye, Lee, Yoonjin

“…-) optimal binary linear codes from our code families. Furthermore, we produce support t-designs (<inline-formula> <tex-math notation="LaTeX"> t = 2</tex-math></inline-formula> or 3…”
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Three New Families of Binary AFER-Optimal Linear Codes by Tong, Tingting, Hu, Sihuang

“… In this paper, we propose novel approaches, different from existing methods, to produce three new families of binary optimal linear codes with the smallest possible error coefficients…”
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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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Optimal binary linear codes of length ⩽30 by Jaffe, David B.

“…For n⩽30, we determine when an [n,k,d] (binary linear) code exists, and we classify optimal [n,k,d…”
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An optimal binary linear functional-repair storage code with efficient repair related to PG(2,8): An optimal functional-repair storage code by Hollmann, Henk D. L., Ke, Junming, Riet, Ago-Erik

“… bound, different from the MSR and MBR points. Here we present another such code, based on a vector space partition of a 9-dimensional binary space into 73 subspaces of dimension 3 that is strongly related to the projective plane PG(2,8…”
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Optimal binary LCD codes by Bouyuklieva, Stefka

“…Linear complementary dual codes (shortly LCD codes) are codes whose intersections with their dual codes are trivial…”
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Binary optimal linear codes with various hull dimensions and entanglement-assisted QECCs by Kim, Jon-Lark

“…The hull of a linear code C is the intersection of C with its dual. To the best of our knowledge, there are very few constructions of binary linear codes with the hull dimension…”
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A Class of Distance-Optimal Binary Linear Codes With Flexible Parameters by Tang, Deng, Fan, Cuiling

“… We determine the weight distributions of all the generated binary linear codes and, most notably, mathematically prove that all these codes are distance-optimal…”
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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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An optimal binary linear functional-repair storage code with efficient repair related to PG(2,8) by Hollmann, Henk D. L, Ke, Junming, Riet, Ago-Erik

“… bound, different from the MSR and MBR points. Here we present another such code, based on a vector space partition of a 9-dimensional binary space into 73 subspaces of dimension 3 that is strongly related to the projective plane PG(2,8…”
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An optimal binary linear functional-repair storage code with efficient repair related to$$\textrm{PG}(2,8) by Hollmann, Henk D. L., Ke, Junming, Riet, Ago-Erik

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Optimal Binary Linear Complementary Pairs of Codes by Choi, Whan-Hyuk, Güneri, Cem, Kim, Jon-Lark, Özbudak, Ferruh

“… Motivated by this, we study binary LCPs of codes. We describe a sufficient condition for binary LCPs of codes which are not optimal…”
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Projection Decoding of Some Binary Optimal Linear Codes of Lengths 36 and 40 by Galvez, Lucky, Kim, Jon-Lark

“… We show that two binary optimal [ 36 , 19 , 8 ] linear codes and two binary optimal [ 40 , 22 , 8 ] codes have an efficient decoding algorithm…”
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Optimal binary and ternary linear codes with hull dimension one by Mankean, Todsapol, Jitman, Somphong

“… Optimal linear [ n , 2 , d ] q codes with hull dimension one are presented for all positive integers n ≥ 3 and q ∈ { 2 , 3 } . Moreover, for q…”
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Optimal Binary Linear Complementary Pairs from Solomon-Stiffler Codes by Guneri, Cem

“… For binary codes, they proved that the security parameter of a linear complementary pair of codes is lower bounded by d L - 1. Choi et al…”
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Two Families of Optimal Binary Linear Complementary Pairs of Codes by Li, Xia, Li, Zhaole

“…The optimal security parameters for binary linear complementary pair (LCP) codes are open. Inspired by this, we study LCPs of codes…”
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Infinite Families of Optimal Linear Codes Constructed From Simplicial Complexes by Hyun, Jong Yoon, Lee, Jungyun, Lee, Yoonjin

“… We construct infinite families of optimal binary linear codes <inline-formula> <tex-math notation="LaTeX"> C_(Δ ᶜ)</tex-math></inline-formula> constructed from simplicial complexes…”
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Constructions of Optimal Binary Locally Recoverable Codes via a General Construction of Linear Codes by Luo, Gaojun, Cao, Xiwang

“… The aim of this paper is to construct optimal binary locally recoverable codes meeting the alphabet-dependent bound…”
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