77 research outputs found

    On deep holes of generalized Reed-Solomon codes

    Full text link
    Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word uu is a deep hole of the standard Reed-Solomon codes [qβˆ’1,k]q[q-1, k]_q if its Lagrange interpolation polynomial is the sum of monomial of degree qβˆ’2q-2 and a polynomial of degree at most kβˆ’1k-1. In this paper, we extend this result by giving a new class of deep holes of the generalized Reed-Solomon codes.Comment: 5 page

    Asymptotic behavior of the least common multiple of consecutive reducible quadratic progression terms

    Full text link
    Let ll and mm be two integers with l>mβ‰₯0l>m\ge 0, and let f(x)f(x) be the product of two linear polynomials with integer coefficients. In this paper, we show that log⁑lcmmn<i≀ln{f(i)}=An+o(n)\log {\rm lcm}_{mn<i\le ln}\{f(i)\}=An+o(n), where AA is a constant depending only on ll, mm and ff.Comment: 13 page
    • …
    corecore