Introduction to finite fields and their applications
Introduction to finite fields and their applications
Shift Register Sequences
On Choice of Connection-Polynominals for LFSR-Based Stream Ciphers
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Multiples of Primitive Polynomials over GF(2)
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Variable Strength Interaction Testing of Components
COMPSAC '03 Proceedings of the 27th Annual International Conference on Computer Software and Applications
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Journal of Combinatorial Theory Series B
Results on multiples of primitive polynomials and their products over GF(2)
Theoretical Computer Science
The test suite generation problem: Optimal instances and their implications
Discrete Applied Mathematics
Division of trinomials by pentanomials and orthogonal arrays
Designs, Codes and Cryptography
On the Distribution of Sums of Successive Bits of Shift-Register Sequences
IEEE Transactions on Computers
A Practical Key Recovery Attack on Basic TCHo
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
TCHo: a hardware-oriented trapdoor cipher
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Orthogonal Arrays, Primitive Trinomials, and Shift-Register Sequences
Finite Fields and Their Applications
Interleaver design for turbo codes
IEEE Journal on Selected Areas in Communications
| Hi-index | 0.00 |
Consider a maximum-length shift-register sequence generated by a primitive polynomial f over a finite field. The set of its subintervals is a linear code whose dual code is formed by all polynomials divisible by f. Since the minimum weight of dual codes is directly related to the strength of the corresponding orthogonal arrays, we can produce orthogonal arrays by studying divisibility of polynomials. Munemasa (Finite Fields Appl 4(3):252---260, 1998) uses trinomials over $${\mathbb{F}_2}$$ to construct orthogonal arrays of guaranteed strength 2 (and almost strength 3). That result was extended by Dewar et al. (Des Codes Cryptogr 45:1---17, 2007) to construct orthogonal arrays of guaranteed strength 3 by considering divisibility of trinomials by pentanomials over $${\mathbb{F}_2}$$ . Here we first simplify the requirement in Munemasa's approach that the characteristic polynomial of the sequence must be primitive: we show that the method applies even to the much broader class of polynomials with no repeated roots. Then we give characterizations of divisibility for binomials and trinomials over $${\mathbb{F}_3}$$ . Some of our results apply to any finite field $${\mathbb{F}_q}$$ with q elements.