On uniform distribution of sequences inGF {q,x } and [GFq,x]

Summary Analogs are proved for sequences in Φ=GF[q, x] and Φ′=GF {q, x } of results proved in 1962 by C.L. Vanden Eynden concerning uuiform distribution of sequence of integers related to sequences of real numbers. The concept of uniform distribution (mod m), m an integer, in Vanden Eynden's work is sometimes replaced here by modified forms of uniform distribution (mod M) M ∈ Φ. Supported by NSF Research Grant GP 6515. Entrata in Redazione il 13 giugno 1969.     

Arithmetic functions associated with unitary divisors inGF[q,x] I

Summary The unitary divisor concept is extended to GF[q, x] and the properties of some elementary functions are obtained. Entrata in Redazione il 9 ottobre 1969.     

Uniform distribution of polynomial-generated sequences inGF[q,x]

Summary Analogs are proved for sequences in Φ=GF[q, x], the ring of polynomials in x over a finite field of q elements, of results of Niven, Zane, and Cavior concerning uniform distribution of sequences of integers generated by polynomials with integer coefficients. The uniform distribution (mod m), m an integer, in these papers is replaced here by a concept called weak uniform distribution (mod M), M ε Φ. Supported byNSF Research GrantGP 6515. Entrata in Redazione il 21 settembre 1968.     

当$4q^{5}-5q^{4}-2q+1\leq d \leq 4q^{5}-5q^{4}-q$时$[g_{q}(6,d),6,d]_{q}$码的不存在性

证明了对于q≥17,当4q~5-5q~4-2q+1≤d≤4q~5-5q~4-q时,不存在达到Griesmer界的[n,k,d]_q码.此结果推广了Cheon等人在2005年和2008年的非存在性定理.     

On codes over $$\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}$$

In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring \(R=\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}\), where \(v^{3}=v\), for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over \(\mathbb {F}_q\) and extend these to codes over R.     

Counting domains in {p,q} tessellations

For any given regular {p,q} tessellation in the hyperbolic plane, we compute the number of vertices and tiles to be found as we distance from a given point, enabling a complete characterization of the asymptotic behavior.     

The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in $$mathbb {F}_{q}[T]$$ F q [ T ]

The Ramanujan Journal - In this paper, we extend to the function field setting the heuristics formerly developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments of...     

The Cauchy Harish-Chandra Integral, for the pair \mathfrak{u}_{p,q} ,\mathfrak{u}_1

For the dual pair considered, the Cauchy Harish-Chandra Integral, as a distribution on the Lie algebra, is the limit of the holomorphic extension of the reciprocal of the determinant. We compute that limit explicitly in terms of the Harish-Chandra orbital integrals.      

On the Diophantine equation $$Cx^{2}+D=2y^{q}$$ C x 2 + D = 2 y q

The Ramanujan Journal - Let C and D denote positive integers such that $$CD>1$$ . In this paper we investigate the solvability of the Diophantine equation $$Cx^{2}+D=2y^{q}$$ , in positive...     

Zeta-like multizeta values for mathbb{F}_q [t]

We prove and conjecture several relations between multizeta values for F _q [t], focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular, we describe them conjecturally fully for q = 2, or more generally for any q for ‘even’ weight (‘eulerian’ tuples). We provide some data in support of the guesses.     

Nonexistence of generalized bent functions from $$\mathbb {Z}_{2}^{n}$$ to $$\mathbb {Z}_{m}$$Zm

In this paper, several nonexistence results on generalized bent functions \(f:\mathbb {Z}_{2}^{n} \rightarrow \mathbb {Z}_{m}\) are presented by using the knowledge on cyclotomic number fields and their imaginary quadratic subfields.     

Improved algorithms for finding low-weight polynomial multiples in \mathbb {F}_{2}^{}[x] and some cryptographic applications

In this paper we present an improved algorithm for finding low-weight multiples of polynomials over the binary field using coding theoretic methods. The associated code defined by the given polynomial has a cyclic structure, allowing an algorithm to search for shifts of the sought minimum-weight codeword. Therefore, a code with higher dimension is constructed, having a larger number of low-weight codewords and through some additional processing also reduced minimum distance. Applying an algorithm for finding low-weight codewords in the constructed code yields a lower complexity for finding low-weight polynomial multiples compared to previous approaches. As an application, we show a key-recovery attack against  that has a lower complexity than the chosen security level indicate. Using similar ideas we also present a new probabilistic algorithm for finding a multiple of weight 4, which is faster than previous approaches. For example, this is relevant in correlation attacks on stream ciphers.