Asymptotically good homological error correcting codes
نویسندگان
چکیده
منابع مشابه
Homological Error Correcting Codes and Systolic Geometry
In my masters thesis I prove a square root bound on the distance of homological codes that come from two dimensional surfaces, as a result of the systolic inequality. I also give a detailed version of M.H. Freedman's proof that due to systolic freedom, this bound does not hold in higher dimensions.
متن کاملGood quantum error-correcting codes exist.
A quantum error-correcting code is defined to be a unitary mapping ~encoding! of k qubits ~two-state quantum systems! into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-co...
متن کاملAsymptotically Good Codes Correcting Insertions, Deletions, and Transpositions (Preliminary Version)
We present simple, polynomial-time encodable and decodable codes which are asymptotically good for channels allowing insertions, deletions and transpositions. As a corollary, they achieve exponential error probability in a stochastic model of insertion-deletion.
متن کاملAsymptotically Good Low-Rate Error-Correcting Codes through Pseudo-Random Graphs
A new technique, based on the pseudo-random properties of certain graphs, known as expanders, is used to obtain new simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling and then regrouping the code coordinates. For any fixed (small) rate, and for sufficiently large alphabet, the codes ...
متن کاملFaster construction of asymptotically good unit-cost error correcting codes in the RAM model
Assuming we are in a Word-RAM model with word size w, we show that we can construct in o(w) time an error correcting code with a constant relative positive distance that maps numbers of w bits into Θ(w)-bit numbers, and such that the application of the error-correcting code on any given number x ∈ [0, 2w − 1] takes constant time. Our result improves on a previously proposed error-correcting cod...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra Combinatorics Discrete Structures and Applications
سال: 2019
ISSN: 2148-838X
DOI: 10.13069/jacodesmath.617235