The independence of two randomness properties of sequences over finite fields
β Scribed by Harald Niederreiter
- Book ID
- 113689543
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 208 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0885-064X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let k=GF(q) be the finite field of order q. Let f 1 (x), f 2 (x) # k[x] be monic relatively prime polynomials satisfying n=deg f 1 >deg f 2 0 and f 1 (x)Γf 2 (x){ g 1 (x p )Γg 2 (x p ) for any g 1 (x), g 2 (x) # k[x]. Write Q(x)= f 1 (x)+tf 2 (x) and let K be the splitting field of Q(x) over k(t). L
Let M be a random n = n -matrix over GF q such that for each entry M in i j w x Ε½ . M and for each nonzero field element β£ the probability Pr M s β£ is pr q y 1 , where i j ## Ε½ . p slog n y c rn and c is an arbitrary but fixed positive constant. The probability for a Ε½ . matrix entry to be zero