相关论文: New Asymptotic Metrics for Relative Generalized Ha…
Relative generalized Hamming weights (RGHWs) of a linear code respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the code. They can be used to express the information leakage of the secret…
Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper we elaborate on the implication of these parameters and we devise a method to estimate…
Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes. In those works the focus is on full privacy and full…
The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…
In [4] Camps-Moreno et al. treated (relative) generalized Hamming weights of codes from extended norm-trace curves and they gave examples of resulting good asymmetric quantum error-correcting codes employing information on the relative…
The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. In this paper, we investigate the generalized Hamming weights of two classes of linear codes constructed from defining sets and determine them completely…
We generalize the Brouwer-Zimmermann algorithm, which is the most efficient general algorithm for computing the minimum distance of a random linear code, to the case of generalized Hamming weights. We also adapt this algorithm to compute…
The generalized Hamming weight (GHW) $d_r(C)$ of linear codes $C$ is a natural generalization of the minimum Hamming distance $d(C)(=d_1(C))$ and has become one of important research objects in coding theory since Wei's originary work [23]…
Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${\cal C}$, identify…
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes under some certain conditions, where $q$ is a power…
The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we…
The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. GHWs are of great interest in many applications since they convey detailed information of linear codes. In this paper, we continue the work of [10] to study…
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network, which restricts…
Coset constructions of $q$-ary Reed-Muller codes can be used to store secrets on a distributed storage system in such a way that only parties with access to a large part of the system can obtain information while still allowing for local…
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes used for this purpose were linear over a larger field than that used on the network. In this work, we introduce new…
Aligning large language models (LLMs) with human preferences through reinforcement learning (RLHF) can lead to reward hacking, where LLMs exploit failures in the reward model (RM) to achieve seemingly high rewards without meeting the…
We consider linear codes over some fixed finite field extension over an arbitrary finite field. Gabidulin introduced rank metric codes, by endowing linear codes over the extension field with a rank weight over the base field and studied…
An $(n,k,r)$ \emph{locally repairable code} (LRC) is an $[n,k,d]$ linear code where every code symbol can be repaired from at most $r$ other code symbols. An LRC is said to be optimal if the minimum distance attains the Singleton-like bound…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…