Cryptography and Communications
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A new binary (17,4,5) constant weight code
Cryptography and Communications - Tập 15 - Trang 443-453 - 2022
We describe a binary (17,4,5) constant weight code with 444 codewords, thus improving the lower bound for A(17,4,5) from 441 to 444. The code was discovered by a computer search implementing a new stochastic local search algorithm for the maximum independent set problem. The algorithm suggested is based on Generic Scuba Search, which is a known hybrid local search method exploiting neutrality in s......
Five classes of optimal two-weight linear codes
Cryptography and Communications - Tập 10 - Trang 1119-1135 - 2017
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes, data storage systems, strongly regular graphs and some other fields. Two-weight linear codes are particularly interesting since they are closely related to finite geometry, combinatorial designs, graph theory. In this paper, we propose five classes of two-Lee-weight codes over the ring
......
Locally repairable codes with multiple repair sets based on packings of block size 4
Cryptography and Communications -
Symbolic dynamics and rotation symmetric Boolean functions
Cryptography and Communications - Tập 14 - Trang 1091-1115 - 2022
We identify the weights wt(fn) of a family {fn} of rotation symmetric Boolean functions with the cardinalities of the sets of n-periodic points of a finite-type shift, recovering the second author’s result that said weights satisfy a linear recurrence. Similarly, the weights of idempotent functions fn defined on finite fields can be recovered as the cardinalities of curves over those fields and he......
Polyphase zero correlation zone sequences from generalised bent functions
Cryptography and Communications - Tập 12 - Trang 325-335 - 2019
Sequence families with zero correlation zone (ZCZ) have been extensively studied in recent years due to their important applications in quasi-synchronous code-division multiple-access (QS-CDMA) systems. To accommodate multiuser environments, multiple ZCZ sequence sets with low inter-set cross-correlation are expected. In this paper, we propose a construction of polyphase ZCZ sequences based on gen......
A number theoretic view on binary shift registers
Cryptography and Communications - Tập 14 - Trang 1067-1080 - 2022
We describe a number theoretic view on binary shift registers. We illustrate this approach on some basic shift registers by revisiting known and obtaining new results, which we prove using tools from basic number theory, including modular arithmetic.
Constructing new superclasses of bent functions from known ones
Cryptography and Communications - Tập 14 - Trang 1229-1256 - 2022
Some recent research articles (Zhang et al. in Lecture Notes in Computer Science, 10194, 298-313. (2017), Zhang et al. in Discret. Appl. Math. 285(1), 458-472. (2020)) addressed an explicit specification of indicators that specify bent functions in the so-called
$${\mathcal C}$$
and
......
Solving $x+x^{2^{l}}+\cdots +x^{2^{ml}}=a$ over $\mathbb {F}_{2^{n}}$
Cryptography and Communications - Tập 12 - Trang 809-817 - 2020
This paper presents an explicit representation for the solutions of the equation
${\sum }_{i=0}^{\frac kl-1}x^{2^{li}} = a \in \mathbb {F}_{2^{n}}$
for any given positive integers k, l with l|k and n, in the closed field
${\overline {\mathbb {F}_{2}}}$
and in the finite field
$\mathbb {F}_{2^{n}}$
. As a by-product of our study, we are able to completely characterize the a’s for which this......
Invariants for EA- and CCZ-equivalence of APN and AB functions
Cryptography and Communications - Tập 13 - Trang 995-1023 - 2021
An (n,m)-function is a mapping from
${\mathbb {F}_{2}^{n}}$
to
${\mathbb {F}_{2}^{m}}$
. Such functions have numerous applications across mathematics and computer science, and in particular are use......
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