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pro vyhledávání: '"14g50"'
This study aims to determine the algebraic structures of $\alpha$-constacyclic codes of length $3p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$, for a prime $p \neq 3.$ For
Externí odkaz:
http://arxiv.org/abs/2412.17697
Let $p$ be an odd prime. In this paper, we have determined the Hamming distances for constacyclic codes of length $2p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$. Also thei
Externí odkaz:
http://arxiv.org/abs/2412.16043
Autor:
Kawakita, Motoko Qiu
We find that non-hyperelliptic generalised Howe curves and their twists of genus 5 attain the Hasse-Weil-Serre bound over some finite fields of order p, p^2 or p^3 for a prime p. We are able to decompose their Jacobians completely under certain assum
Externí odkaz:
http://arxiv.org/abs/2412.03071
The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the wire-tap channel of type II, $t$-resilient functions, bounding the card
Externí odkaz:
http://arxiv.org/abs/2411.13375
Finding a low-weight multiple (LWPM) of a given polynomial is very useful in the cryptanalysis of stream ciphers and arithmetic in finite fields. There is no known deterministic polynomial time complexity algorithm for solving this problem, and the m
Externí odkaz:
http://arxiv.org/abs/2410.10224
Autor:
Goren, Eyal Z., Love, Jonathan R.
This paper contains a survey of supersingular isogeny graphs associated to supersingular elliptic curves and their various applications to cryptography. Within limitation of space, we attempt to address a broad audience and make this part widely acce
Externí odkaz:
http://arxiv.org/abs/2410.06123
Autor:
Aguilar, Konrad, Álvarez, Angelynn, Ardila, René, Ocal, Pablo S., Avila, Cristian Rodriguez, Várilly-Alvarado, Anthony
A code is locally recoverable when each symbol in one of its code words can be reconstructed as a function of $r$ other symbols. We use bundles of projective spaces over a line to construct locally recoverable codes with availability; that is, evalua
Externí odkaz:
http://arxiv.org/abs/2409.04201
We determine the higher weight spectra of $q$-ary Reed-Muller codes $C_q=RM_q(2,2)$ for all prime powers $q$. This is equivalent to finding the usual weight distributions of all extension codes of $C_q$ over every field extension of $F_q$ of finite d
Externí odkaz:
http://arxiv.org/abs/2408.02548
In recent years, linear complementary pairs (LCP) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory and cryptography. In this work, we construct explicit LCPs of codes and
Externí odkaz:
http://arxiv.org/abs/2407.05845
We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules over global fields, and Dirichlet Theorem on polynomial arithmetic progressions. Using our methods, we obtain a new infinite family of optimal
Externí odkaz:
http://arxiv.org/abs/2407.06081