Search results
Results From The WOW.Com Content Network
Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley. [1] [2] Berlekamp was widely known for his work in computer science, coding theory and combinatorial game theory . Berlekamp invented an algorithm to factor polynomials and the Berlekamp ...
In mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields ). The algorithm consists mainly of matrix reduction and polynomial GCD computations. It was invented by Elwyn Berlekamp in 1967. It was the dominant algorithm for solving the ...
The Berlekamp–Welch algorithm, also known as the Welch–Berlekamp algorithm, is named for Elwyn R. Berlekamp and Lloyd R. Welch. This is a decoder algorithm that efficiently corrects errors in Reed–Solomon codes for an RS ( n, k ), code based on the Reed Solomon original view where a message is used as coefficients of a polynomial or used ...
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field. The field requirement means that the Berlekamp–Massey algorithm requires all non-zero ...
The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched. [citation needed] Algebraic coding theory is basically divided into two major types of codes: [citation needed] Linear block codes; Convolutional codes
Lee distance. In coding theory, the Lee distance is a distance between two strings and of equal length n over the q -ary alphabet {0, 1, …, q − 1 } of size q ≥ 2. It is a metric [1] defined as. If q = 2 or q = 3 the Lee distance coincides with the Hamming distance, because both distances are 0 for two single equal symbols and 1 for two ...
In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials over the field with elements. The method was discovered by Elwyn Berlekamp in 1970 [ 1 ] as an auxiliary to the algorithm for polynomial factorization over finite fields.
In coding theory, rank codes (also called Gabidulin codes) are non-binary [1] linear error-correcting codes over not Hamming but rank metric. They described a systematic way of building codes that could detect and correct multiple random rank errors. By adding redundancy with coding k -symbol word to a n -symbol word, a rank code can correct ...