Nyob rau hauv tus lej cyclic?

2024 Tus sau: Fiona Howard | [email protected]. Kawg hloov kho: 2024-01-10 06:38

Nyob rau hauv coding txoj kev xav, ib tug cyclic code yog a thaiv code, qhov twg lub voj voog ntawm txhua tus codeword muab lwm lo lus uas belongs rau code. Lawv yog cov kev ua yuam kev-kho cov lej uas muaj cov cuab yeej algebraic uas yooj yim rau kev txhim kho kev ua yuam kev thiab kho.

Cyclic codes muab piv txwv yog dab tsi?

Example of a Simple Cyclic Code Xav txog binary code C={000, 110, 011, 101} … Definition (Cyclic Code) A binary code yog cyclic yog tias nws yog ib kab [n, k] code thiab yog tias rau txhua lo lus code (c1, c2, …, cn) ∈ C peb kuj muaj qhov ntawd (cn, c1, …, cn-1) yog dua ib lo lus hauv C.

Yuav ua li cas koj ua pov thawj ib tug cyclic code?

A polynomial code yog cyclic yog tias thiab tsuas yog yog tias nws lub tshuab hluav taws xob polynomial faib xn − 1. r(x)=−h(x)g(x) mod (xn − 1), yog li r(x) ∈ C. Qhov no txhais tau tias r(x)=0, vim tsis muaj lwm lo lus hauv C tuaj yeem muaj qib me dua. deg(g).

Puas yog cyclic codes linear?

Cyclic Code paub tias yog subclass ntawm linear block codes qhov twg cyclic hloov hauv cov khoom ntawm cov codeword ua rau lwm tus lej code.

Yuav ua li cas lub voj voog kab lis kev cai yog encoded?

Set c(x)=xn−km(x) − d(x). Qhov no encoding ua haujlwm, raws li (1) c(x) yog ntau yam ntawm g(x) thiab yog li ntawd ib tug codeword, (2) thawj n − k coefficients ntawm xn−km(x) yog xoom, thiab (3) tsuas yog thawj n − k coefficients ntawm −d(x) yog nonzero (the degree of g(x) yog n − k).