Advances in Mathematics of Communications
November 2017 , Volume 11 , Issue 4
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The weight distribution
For two odd integers
Some families of constant dimension codes arising from Riemann-Roch spaces associated with particular divisors of a curve
In this work, we introduce an active attack on a Group Key Exchange protocol by Burmester and Desmedt. The attacker obtains a copy of the shared key, which is created in a collaborative manner with the legal users in a communication group.
We consider a variation of Construction A of lattices from linear codes based on two classes of number fields, totally real and CM Galois number fields. We propose a generic construction with explicit generator and Gram matrices, then focus on modular and unimodular lattices, obtained in the particular cases of totally real, respectively, imaginary, quadratic fields. Our motivation comes from coding theory, thus some relevant properties of modular lattices, such as minimal norm, theta series, kissing number and secrecy gain are analyzed. Interesting lattices are exhibited.
In this note, we study the classification of
In this paper we study subspace codes with constant intersection dimension (SCIDs). We investigate the largest possible dimension spanned by such a code that can yield non-sunflower codes, and classify the examples attaining equality in that bound as one of two infinite families. We also construct a new infinite family of primitive SCIDs.
In this note, we investigate the performance of optimal double circulant even codes which are not self-dual, as measured by the decoding error probability in bounded distance decoding. To achieve this, we classify the optimal double circulant even codes that are not self-dual which have the smallest weight distribution for lengths up to 72. We also give some restrictions on the weight distributions of (extremal) self-dual [54, 27, 10] codes with shadows of minimum weight 3. Finally, we consider the performance of extremal self-dual codes of lengths 88 and 112.
In this article we count the number of $[n, k]$ generalized Reed-Solomon (GRS) codes, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of $[n, 3]$ MDS codes with $n=6, 7, 8, 9$.
The purpose of this paper is to study the structure of quadratic residue codes over the ring
In Crypto 1996, the Hidden Number Problem was introduced by Boneh and Venkatesan. Howgrave-Graham, Nguyen and Shparlinski (Mathematics of Computation 2003) generalized this problem and called it Hidden Number Problem with Hidden Multiplier (HNPHM). It has application in security analysis of timed-release crypto. They proposed a polynomial time algorithm to solve HNPHM. They showed that one can solve it if absolute error is less than
We consider discrete memoryless channels with input alphabet size
In a first part of this paper, we investigate those Boolean functions satisfying two apparently related, but in fact distinct conditions concerning the algebraic degree:
1. we study those Boolean functions
2. we study those functions whose derivatives
For determining to which extent these two questions are related, we find three classes of Boolean functions: the first class satisfies both conditions, the second class satisfies the first condition but not the second and the third class satisfies the second condition but not the first. We also give for any fixed positive integer
In a second part of the paper, we introduce the notion of second-order-bent function, whose second order derivatives
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