Results 41 to 50 of about 516,863 (164)
How to Find the Equivalence Classes in a Set of Linear Codes in Practice?
MathematicsAn algorithm for equivalence of linear codes over finite fields is presented. Its main advantage is that it can extract exactly one representative from each equivalence class among a large number of linear codes.
Stefka Bouyuklieva, Iliya Bouyukliev
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Entropy, 2023 Nested linear coding is a widely used technique in wireless communication systems for improving both security and reliability. Some parameters, such as the relative generalized Hamming weight and the relative dimension/length profile, can be used to ...
Morteza Shoushtari, Willie Harrison
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, 2015 In an application, where a client wants to obtain many elements from a large database, it is often desirable to have some load balancing. Batch codes (introduced by Ishai et al. in STOC 2004) make it possible to do exactly that: the large database is divided between many servers, so that the client has to only make a small number of queries to every ...
Helger Lipmaa, Vitaly Skachek
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A Class of the Hamming Weight Hierarchy of Linear Codes with Dimension 5
Tsinghua Science and Technology, 2014 The weight hierarchy of a [n,k;q] linear code C over Fq is the sequence (d1,⋯,dr,⋯,dk), where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight
Guoxiang Hu +3 more
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On the Extendability of Linear Codes
Finite Fields and Their Applications, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Algorithms, 2019 A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers ( s ≥ 2 ) of all nonzero elements in G F ( p m ) , where p ≥ 2 is prime.
Dean Crnković +2 more
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Matrix Factorization and Some Fast Discrete Transforms
AxiomsIn this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh ...
Iliya Bouyukliev +2 more
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Squares of Random Linear Codes [PDF]
IEEE Transactions on Information Theory, 2015 Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code "typically" fill the whole space?
I. Cascudo (Ignacio) +3 more
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Ternary Linear Codes and Quadrics [PDF]
The Electronic Journal of Combinatorics, 2009 For an $[n,k,d]_3$ code ${\cal C}$ with $gcd(d,3)=1$, we define a map $w_G$ from $\Sigma={\rm PG}(k-1,3)$ to the set of weights of codewords of ${\cal C}$ through a generator matrix $G$. A $t$-flat $\Pi$ in $\Sigma$ is called an $(i,j)_t$ flat if $(i,j)=(|\Pi \cap F_0|,|\Pi \cap F_1|)$, where $F_0 = \{P \in \Sigma | w_G(P) \equiv 0 \pmod{3 ...
Yuri Yoshida, Tatsuya Maruta
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Constructions of some secret sharing schemes based on linear codes [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаThere are perfect and ideal threshold secret sharing schemes, for example, Shamir’s secret sharing scheme. For the case of general secret sharing schemes with an arbitrary access structure, it is possible to construct a perfect scheme for any
Ratseev, Sergey Mihailovich
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