Two r × n matrices A and A′ representing the same matroid M over GF (q), where q is a prime power, are projective equivalent representations of M if one can be obtained from the other by elementary row operations and column scaling. Bounds for projective inequivalence are difficult to obtain and are known for only a few special classes of matroids. In this paper we define two matrices A and A′ ...

This contribution describes a squarer architecture for standard basis field representation. This architecture is based on the observation that one can transform a squaring operation in GF (2 m) into an addition and a multiplication of two elements of special form, which computational time depends on the form of the field polynomial.

The linear complexity of a periodic sequence over GF (pm) plays an important role in cryptography and communication [12]. In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal connection polynomial of a period un sequence over GF (pm) to the computation of the linear complexities and minimal connection polynomials of u period n sequences. T...

when studying russian morphology, one can distinguish two categories. these categories are “grammatical” and “lexico-grammatical”. grammatical categories can be specified through a series of grammatical features of words. considering different criteria, russian grammarians and linguists divide grammatical categories of their language into different types. in determining lexico-grammatical types...

We describe a new deterministic algorithm for the problem of constructing k th power nonresidues in nite elds GF p where p is prime and k is a prime divisor of p We prove under the assumption of the Extended Riemann Hypothesis ERH that for xed n and p our algorithm runs in polynomial time Unlike previous algorithms for this problem this polynomial time bound holds even if k is very large More g...

Many studies reveal a strong impact of childhood maltreatment on language development, mainly resulting in shorter utterances, less rich vocabulary, or a delay in grammatical complexity. However, different theories suggest the possibility for resilience-a positive adaptation to an otherwise adverse environment-in children who experienced childhood maltreatment. Here, we investigated different m...

For fixed positive integers k, q, r with q a prime power and large m, we investigate matrices with m rows and a maximum number Nq(m, k, r) of columns, such that each column contains at most r nonzero entries from the finite field GF (q) and each k columns are linearly independent over GF (q). For even integers k ≥ 2 we obtain the lower bounds Nq(m, k, r) = Ω(m kr/(2(k−1))), and Nq(m, k, r) = Ω(...

This contribution describes a squarer architecture for standard basis field representation. This architecture is based on the observation that one can transform a squaring operation in GF (2m) into an addition and a multiplication of two elements of special form, which computational time depends on the form of the field polynomial.

We study the correlation between low-degree GF (2) polynomials p and explicit functions. Our main results are the following: I We prove that theModm function on n bits has correlation at most exp ( −Ω ( n/4d )) with any GF (2) polynomial of degree d, for any fixed odd integer m. This improves on the previous exp ( −Ω ( n/8d )) bound by Bourgain (C. R. Acad. Sci. Paris, 2005) and Green et al. (C...