✦ LIBER ✦

The number of solutions of certain matric equations over a finite field

✍ Scribed by L. Carlitz

Publisher: John Wiley and Sons
Year: 1973
Tongue: English
Weight: 125 KB
Volume: 56
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19730560109

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On the Number of Solutions of Diagonal E

On the Number of Solutions of Diagonal Equations over a Finite Field

✍ Qi Sun; Ping-Zhi Yuan 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 181 KB

In this paper, we give a reduction theorem for the number of solutions of any diagonal equation over a finite field. Using this reduction theorem and the theory of quadratic equations over a finite field, we also get an explicit formula for the number of solutions of a diagonal equation over a finit

On the Number of Solutions of a Linear E

On the Number of Solutions of a Linear Equation over Finite Sets

✍ Vsevolod F. Lev 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 300 KB

The largest possible number of representations of an integer in the k-fold sumset kA=A+ } } } +A is maximal for A being an arithmetic progression. More generally, consider the number of solutions of the linear equation where c i {0 and \* are fixed integer coefficients, and where the variables a i

The rank of sparse random matrices over

The rank of sparse random matrices over finite fields

✍ Johannes Blömer; Richard Karp; Emo Welzl 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB 👁 2 views

Let M be a random n = n -matrix over GF q such that for each entry M in i j w x Ž . M and for each nonzero field element ␣ the probability Pr M s ␣ is pr q y 1 , where i j ## Ž . p slog n y c rn and c is an arbitrary but fixed positive constant. The probability for a Ž . matrix entry to be zero

On the Ranks of Skew Centrosymmetric Mat

On the Ranks of Skew Centrosymmetric Matrices over Finite Fields

✍ William C. Waterhouse 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 169 KB

The Number of Permutation Polynomials of

The Number of Permutation Polynomials of a Given Degree Over a Finite Field

✍ Pinaki Das 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 139 KB

We relate the number of permutation polynomials in F q ½x of degree d q À 2 to the solutions ðx 1 ; x 2 ; . . . ; x q Þ of a system of linear equations over F q , with the added restriction that x i =0 and x i =x j whenever i=j. Using this we find an expression for the number of permutation polynomi

On the Geometry of Hermitian Matrices of

On the Geometry of Hermitian Matrices of Order Three Over Finite Fields

✍ Antonio Cossidente; Alessandro Siciliano 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 139 KB

Some geometry of Hermitian matrices of order three over GF(q 2 ) is studied. The variety coming from rank 2 matrices is a cubic hypersurface M 3 7 of PG(8, q) whose singular points form a variety H corresponding to all rank 1 Hermitian matrices. Beside M 3 7 turns out to be the secant variety of H.