Solving underdetermined systems with error-correcting codes
نویسندگان
چکیده
منابع مشابه
Solving underdetermined systems with error-correcting codes
In an underdetermined system of equations Ax = y, where A is an m × n matrix, only u of the entries of y with u < m are known. Thus Ejw, called ‘measurements’, are known for certain j ∈ J ⊂ {0, 1, . . . ,m−1} where {Ei, i = 0, 1, . . . ,m−1} are the rows of A and |J | = u. It is required, if possible, to solve the system uniquely when x has at most t non-zero entries with u ≥ 2t. Here such syst...
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 کاملConstructing Quantum Error-Correcting Codes for p-State Systems from Classical Error-Correcting Codes∗
Quantum error-correcting codes have attracted much attention. Among many research articles, the most general and systematic construction is the so called stabilizer code construction [6] or additive code construction [2], which constructs a quantum error-correcting code as an eigenspace of an Abelian subgroup S of the error group. Thereafter Calderbank et al. [3] proposed a construction of S fr...
متن کاملFinite-connectivity systems as error-correcting codes.
We investigate the performance of parity check codes using the mapping onto Ising spin systems proposed by Sourlas [Nature (London) 339, 693 (1989); Europhys. Lett. 25, 159 (1994)]. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C checks per message bit. We show, using the replica method, that these codes saturate Shan...
متن کاملExtending Local Learners with Error-correcting Output Codes Extending Local Learners with Error-correcting Output Codes
Error-correcting output codes (ECOCs) represent classes with a set of output bits, where each bit encodes a binary classiication task corresponding to a unique partition of the classes. Algorithms that use ECOCs learn the function corresponding to each bit, and combine them to generate class predictions. ECOCs can reduce both variance and bias errors for multiclass classiication tasks when the ...
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: International Journal of Information and Coding Theory
سال: 2017
ISSN: 1753-7703,1753-7711
DOI: 10.1504/ijicot.2017.10005825