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Everything about Berlekamp's algorithm
Method in computational algebra
In mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite 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 problem until the Cantor–Zassenhaus algorithm of 1981. It is currently implemented in many well-known computer algebra systems. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Berlekamp's algorithmA 5-minute orientation
- Skim a recent paper: Decoding of cyclic codes over quaternion integers by modified Berlekamp–Massey algorithmInfluential work since 2022
- Pick up a classic book: Sequences and their ApplicationsThe most-reprinted book on the subject
- Read the landmark paper: A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codesCited 149 times
- Go sideways: Berlekamp–Rabin algorithmA closely related topic
- Go sideways: Factorization of polynomials over finite fieldsA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes
Extension of the Berlekamp-Massey algorithm to N dimensions
VLSI design of inverse-free Berlekamp—Massey algorithm
A simple derivation of the Berlekamp- Massey algorithm and some applications (Corresp.)
Analysis of the Berlekamp-Massey Linear Feedback Shift-Register Synthesis Algorithm
A fast parallel implementation of a Berlekamp-Massey algorithm for algebraic-geometric codes
Decoding binary 2-D cyclic codes by the 2-D Berlekamp-Massey algorithm
Implementation of Berlekamp—Massey algorithm without inversion
🆕 Influential since 2022
Decoding of cyclic codes over quaternion integers by modified Berlekamp–Massey algorithm
Parallel Welch–Berlekamp Algorithm
Modification of the Berlekamp-Massey algorithm for explicable knowledge extraction by SIEM-agents
Optimized Error Detection and Correction in ATM Networks Using the Enhanced Berlekamp Massey Algorithm With Hybrid Automatic Repeat Request
Pattern sets for $$\mathbb {F}_q$$-sequences invariant under the continued fraction operator K (the Berlekamp-Massey algorithm)
đź“š Books worth reading
Sequences and their ApplicationsC. Ding · 1999
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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