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Matrix 2 of 5 is a subset of two-out-of-five codes. Unlike Industrial 2 of 5 code, Matrix 2 of 5 can encode data not only with black bars but with white spaces. Matrix 2 of 5 [2] [3] was developed in 1970-х by Nieaf Co. [4] in The Netherlands and commonly was uses for warehouse sorting, photo finishing, and airline ticket marking. [5]
2 of 5 barcode (non-interleaved) POSTNET barcode. A two-out-of-five code is a constant-weight code that provides exactly ten possible combinations of two bits, and is thus used for representing the decimal digits using five bits. [1] Each bit is assigned a weight, such that the set bits sum to the desired value, with an exception for zero.
In this code, 5 physical qubits are used to encode the logical qubit. [2] With X {\displaystyle X} and Z {\displaystyle Z} being Pauli matrices and I {\displaystyle I} the Identity matrix , this code's generators are X Z Z X I , I X Z Z X , X I X Z Z , Z X I X Z {\displaystyle \langle XZZXI,IXZZX,XIXZZ,ZXIXZ\rangle } .
A multidimensional parity-check code (MDPC) is a type of error-correcting code that generalizes two-dimensional parity checks to higher dimensions. It was developed as an extension of simple parity check methods used in magnetic recording systems and radiation-hardened memory designs .
The generalized Poincaré conjecture is true topologically, but false smoothly in most dimensions. In fact, for odd dimensions, the smooth Poincaré conjecture is only true in dimensions 1, 3, 5 and 61. In even dimensions it is known that the smooth Poincaré conjecture is true in dimensions 2, 6, 12 and 56.
A self-dual code is one which is its own dual. This implies that n is even and dim C = n/2. If a self-dual code is such that each codeword's weight is a multiple of some constant >, then it is of one of the following four types: [1] Type I codes are binary self-dual codes which are not doubly even.
This extra dimension is a compact set, and construction of this compact dimension is referred to as compactification. In modern geometry, the extra fifth dimension can be understood to be the circle group U(1) , as electromagnetism can essentially be formulated as a gauge theory on a fiber bundle , the circle bundle , with gauge group U(1).
In dimension 5, the smooth classification of simply connected manifolds is governed by classical algebraic topology. Namely, two simply connected, smooth 5-manifolds are diffeomorphic if and only if there exists an isomorphism of their second homology groups with integer coefficients, preserving the linking form and the second Stiefel–Whitney ...