Related papers: Flags of almost affine codes
Starting from Borel's description of the mod-2 cohomology of real flag manifolds, we give a minimal presentation of the cohomology ring for semi complete flag manifolds $F_{k,m}:=F(1,\ldots,1,m)$ where $1$ is repeated $k$ times. The…
We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties. This second part of a two paper series uses this new language, i.e. the double Bruhat graph, to describe certain structure…
In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain…
We consider the wiretap channel, where the individual channel uses have memory or are influenced by an adversary. We analyze the explicit and computationally efficient construction of information-theoretically secure coding schemes which…
We construct a modular scheme which extends codes for wiretap channels of type I for use in wiretap channels of type II. This is done by using a concatenate and permute strategy, wherein multiple uses of the wiretap type I code are…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
A polar coding scheme is introduced in this paper for the wire-tap channel. It is shown that the provided scheme achieves the entire rate-equivocation region for the case of symmetric and degraded wire-tap channel, where the weak notion of…
The wiretap channel is a setting where one aims to provide information-theoretic privacy of communicated data based solely on the assumption that the channel from sender to adversary is "noisier" than the channel from sender to receiver. It…
Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the…
We give a new interpretation and proof of the "quasi-particle" type character formulas for integrable representations of the simply-laced affine Kac-Moody algebras through a new "semi-infinite" construction of such representations. We…
In a point-to-point communication system which consists of a sender, a receiver and a set of noiseless channels, the sender wishes to transmit a private message to the receiver through the channels which may be eavesdropped by a wiretapper.…
We analyze arbitrarily varying classical-quantum wiretap channels.These channels are subject to two attacks at the same time: one passive (eavesdropping), and one active (jamming). We progress on previous works by introducing a reduced…
In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate flags and have been suggested as suitable framework for…
The wiretap channel is a well-studied problem in the physical layer security literature. Although it is proven that the decoding error probability and information leakage can be made arbitrarily small in the asymptotic regime, further…
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…
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…
Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…
In this two-part paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an information-theoretic problem formulation in which two legitimate partners communicate over a quasi-static…