On the Covering Radius of Long Goppa Codes
نویسندگان
چکیده
منابع مشابه
Exponential Sums and Goppa Codes: I
A bound is obtained which generalizes the Carlitz-Uchiyama result, based on a theorem of Bombieri and Weil about exponential sums. This new bound is used to estimate the covering radius of long binary Goppa codes. A new lower bound is also derived on the minimum distance of the dual of a binary Goppa code, similar to that for BCH codes. This is an example of the use of a number-theory bound for...
متن کاملParameters of Goppa codes revisited
We discuss parameters of Goppa codes, such as minimum distance, covering radius, distance distribution, and generalized Hamming weights. By a variation on the exponential sums method and combinatorial arguments, we sharpen known bounds.
متن کاملOne-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...
متن کاملGoppa codes
Absfruct-Goppa described a new class of linear noncyclic errorcorrecting codes in [l] and [2]. This paper is a summary of Goppa’s work, which is not yet available in English.’ We prove the four most important properties of Goppa codes. 1) There exist q-ary Goppa codes with lengths and redundancies comparable to BCH codes. For the same redundancy, the Goppa code is typically one digit longer. 2)...
متن کاملOn the Complexity of Decoding Goppa Codes
-It is shown that i) erasures-and-errors decoding of Goppa codes can be done using O(n log2 n) arithmetic operations, ii) long primitive binary Bose-Chaudhuri-Hocquenghem (BCH) codes can be decoded using O(n log n) arithmetic operations, and iii) Justesen’s asymptotically good codes can be decoded using O(n2) bit operations. These results are based on the application of efficient computational ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995