78 research outputs found
On deep holes of generalized Reed-Solomon codes
Determining deep holes is an important topic in decoding Reed-Solomon codes.
In a previous paper [8], we showed that the received word is a deep hole of
the standard Reed-Solomon codes if its Lagrange interpolation
polynomial is the sum of monomial of degree and a polynomial of degree at
most . 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
Let and be two integers with , and let be the
product of two linear polynomials with integer coefficients. In this paper, we
show that , where is a
constant depending only on , and .Comment: 13 page
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