Three Classes of Optimal Ternary Cyclic Codes and the Weight Distributions of Their Duals

Li, Lanqiang; Zhu, Shixin; Liu, Li

doi:10.1049/cje.2019.04.001

Cited by 4 publications

(2 citation statements)

References 23 publications

(56 reference statements)

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“…Ding and Helleseth [7] constructed several classes of optimal ternary cyclic codes C (1,e) with parameters [3 m − 1, 3 m − 1 − 2m, 4] by using almost perfect nonlinear monomials and some other monomials over F 3 m . Subsequently, many classes of optimal ternary cyclic codes C (1,e) with parameters [3 m − 1, 3 m − 1 − 2m, 4] were constructed successively [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Two Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four

HE,

RAN,

LUO

2024

IEICE Trans. Fundamentals

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This article has been accepted and published on J-STAGE in advance of copyediting. Content is final as presented. LETTER Two classes of optimal ternary cyclic codes with minimum distance fourChao HE † * a) , Xiaoqiong RAN † * b) , Nonmembers, and Rong LUO † * c) , Member SUMMARYCyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let C (t,e) denote the cyclic code with two nonzero α t and α e , where α is a generator of F * 3 m . In this letter, we investigate the ternary cyclic codes with parameters [3 m −1, 3 m −1−2m, 4] based on some results proposed by Ding and Helleseth in 2013. Two new classes of optimal ternary cyclic codes C (t,e) are presented by choosing the proper t and e and determining the solutions of certain equations over F 3 m .

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Section: Introductionmentioning

confidence: 99%

Two Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four

HE,

RAN,

LUO

2024

IEICE Trans. Fundamentals

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“…It might be also worth to mention an interesting direction of researches which aim at reducing the size of NN models through reducing the size of the model parameters themselves through some kind of "quantization". This essentially means to design architectures, training and inference methods for integer arithmetic [110] or even to ternary (∀i w i ∈ {−1, 0, +1}) [140] or binary (∀i w i ∈ {−1, +1}) networks as in [48] or [171].…”

Section: Compressionmentioning

confidence: 99%

Federated Learning of Artificial Neural Networks

Kiss¹

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The training of the most expressive state-of-the-art Machine Learning (ML) models, and especially that one of Artificial Neural Networks (NN) requires a huge amount of training data, along with very significant computation resources. The paradigm of Federated Learning (FL) focuses on the possibilities of collaborative training of ML models in heterogeneous, spatially distributed environment of recent IT infrastructures, dividing the burden of computation among all the stakeholders and leaving the potentially sensitive data at the location of its creation.In this dissertation I am presenting my work relating to the possibilities to alleviate apparent problems of federated training of NNs. For the experienced performance loss we propose to adapt and use stateful optimization techniques for the FL setup. For communication complications of the centralized training we tested a technique to simulate FL in a peer to peer environment. And finally for the privacy issues we present a method to train NNs in an FL environment via a derivative free genetic algorithm. ContributionChapter 1 ContributionIn the research field of federated optimization, in our view, recent works are conducted with the goal in mind to alleviate some of the three main problems of FL algorithms from the original proposals in [129] and [157]. The first of these problems is the observed performance degradation of the learning process, or insufficient accuracy on the side of the end users. The second research direction is about practical questions of implementing these methods, such that resource provisioning, or more concretely, addressing the communication problems in real world network architectures. And the third group of works is seeking to provide stronger privacy guaranties for the users who participate with their data in the training process.In my theses I propose simple techniques to alleviate the three above mentioned issues of FL. Performance degradationThe first problem we examined is the empirical fact that FL of NNs under-performs central training, both in the accuracy of final models, and in the rate of learning. According to our intuition this issue might be relieved at some extent by stateful optimization methods, that have been originally designed to overcome similar problems to those that arises from the characteristics of FL training. Based on our experiments [64,126], presented in Chapter 4, these methods can help to alleviate the performance issues of FL in almost all the examined cases.

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Several classes of optimal cyclic codes with three zeros

Wu,

Liu,

2023

AAECC

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Three Classes of Optimal Ternary Cyclic Codes and the Weight Distributions of Their Duals

Cited by 4 publications

References 23 publications

Two Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four

Two Classes of Optimal Ternary Cyclic Codes with Minimum Distance Four

Federated Learning of Artificial Neural Networks

Several classes of optimal cyclic codes with three zeros

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