
werhoff algoritam

1969ll dutch ganithashaasthranjanaaya jacobus werhoff aadyamaayi prasidheekaricha pishak kandethunnathinulla oru cheksamaanu werhoff algoritam. ellah otta akka pishakukalum, aduthulla rund akkangal ulppedunna ellah transposition pishakukalum kandethunna aadyathe dasaamsha check digit algorithamaayirunnu ithu, atharam oru codil asaadhyamenn akkaalat karuthappettirunnu.
lakshyangal.
check akkam orotta dasaamsha akkamaaya oru dasaamsha coode kandethuka ennathaanu verhoffinte lakshyam-ithu ellah eaka akka pishakukalum aduthulla akkangalude ellah kaimattangalum kandethi. akkaalat, eee kodukalude asthithvamillennathinte thelivukal bays-11 kodukale janapriyamakki, udaaharanathinu aii. ezz. bii. enn check akkatthil.
addehathinte lakshyangalum praayogikamaayirunnu, koodaathe dutch tapal samvidaanathil ninnulla thalsamaya daattaye adisthaanamaakki vividha kodukalude vilayiruthal addeham adisthaanamaakki, vividha tharatthilulla pishakukalkk waited pooyint sisttam upayogichu. vishakalanam pishakukale niravadhi vibhagangalaayi vibhajichu aadyam, ethra akkangal thettaanu ennathukondu; rund akkangal thettullavarkk, "traansposishanukal" ("abb" → "baa"), "erattakal" ("aaa" → 'bibi ")," jump traansposishanukal "(" abc "→" cba ")," phoonetik "(" 1eiii "" "eiii0" ")," jump twins "(" abaa "" "cbc" ") ennivayundu. koodaathe ozhivaakkukayum kootticherkkukayum cheytha akkangalum undu. itharathilulla chila pishakukalude aavruthi cheruthaayirikkaamenkilum, ellah singles traansposishanukalum kandethunnathinulla praadhamika lakshyangalkk purame chila kodukal avayil ninnu prathirodhasheshiyullathaayir.
duchill, samkhyakal saadhaaranayaayi jodikalaayi vaayikkappedunnathinaal, prathyekichum phoonetik pishakukal bhashaaparamaaya phalangal kaanichu; duchill 50 shabdangal 15 nuu samaanamaanengilum 80 18 pole thonnunnilla.
aarr akka samkhyakal udaaharanamaayi edukkumbol, werhoff pishakukalude inipparayunna vargeekaranam report cheythu
vivaranam.
oro akkangaleyum (0 muthal 9 vare) dihedral group formula _ 1-nte gadakangalaayi prathinidheekarikkuka ennathaanu algorithathinte pothuvaaya ashayam. athaayath, akkangale formula _ 1-lake mapp cheyyuka, iva kaikaaryam cheyyuka, thudarnnu akkangalilekku mapp cheyyuka. eee mapping formula _ 3 ayirikkatte
formula _ 4
n-aam akkam formula 5 ayirikkatte, akkangalude ennam formula 6 ayirikkatte.
udaaharanathinu 248 enna coode nalkiyaal formula 6 ennathu 3 umm formula 8 umm aanu. 
ippol kramaparivarthana soothravaakyam _ 9 nirvachikkuka.
soothravaakyam _ 10
udaaharanathinu formula _ 11. mattoru udaaharanam formula _ 13 muthal formula _ 12 aanu.
formula _ 1-nte group pravarthanatthinaayi gunana notteshan upayogichu, check digit oru moolya formula _ 15 aanu.
soothravaakyam _ 16
formula _ 15 vyakthamaayi vipareeta kramappeduthaliloode nalkiyirikkunnu.
soothravaakyam _ 18
udaaharanathinu, 248-nte check akkam 5 aanu. ithu parisodhikkaan, formula _ 1 lake mapping upayogikkuka, munbathe samavaakyathinte lhs-ll cherkkuka.
soothravaakyam _ 20
eee kramappedutthal vegathil vilayiruthaan athu upayogikkuka
soothravaakyam _ 21
athu labhikkaan
soothravaakyam _ 22
ithu aavarthichu gunikkunna athe prathifalanamaanu. prathiphalanangal avayude vipareethamaanennu upayogikkuka.
soothravaakyam _ 23
praayogikamaayi, adisthaana groupil ninnum kramappedutthal sidhaanthathil ninnum aaa pattikakal engane srishtikkaamennu manasilaakkenda aavasyamillaathe lalithamaaya lookup tableukal upayogichaanu algoritam nadappilaakkunnathu. mattu kramamattangalum pravarthikkunnathinaal ithu algorithangalude oru kudumbamaayi kooduthal shariyaayi kanakkaakkappedunnu. phoonetik pishakukalude 95.3% kandethanulla savisheshatha ullathinaal mukalil nalkiyirikkunna prathyeka kramappedutthal savisheshamaanennu verhoffinte kurippukal parayunnu.
lipyantharanathilum transposition pishakukalilum koodaathe mikka eratta, eratta jump, jump transposition, phoonetik pishakukalum ithu kandethunnu ennathaanu algorithathinte shakti.
werhoff algorithathinte pradhana balaheenata athinte sankeernathayaanu. aavashyamaaya kanakkukoottalukal formula _ 24 ll oru soothravaakyamaayi eluppathil prakadippikkaan kazhiyilla. eluppathil kanakkukoottunnathin lookup tableukal aavasyamaanu. samanamaaya gunangalulla daam algoritam samanamaaya oru kodaanu.
table adhishtitha algoritam.
moonnu pattikakal upayogichu werhoff algoritam nadappilaakkaam
oru gunana pattika "dii", oru vipareeta pattika "inv", oru kramaparivarthana pattika "pii".
aadyathe pattika, dii, dihedral grouppaaya dii5 leeii gunanathe adisthaanamaakkiyullathaanu. ithu grouppinte kayley table maathramaan. eee group commutative allennu shradhikkuka, athaayath, "jeey", "keey" ennivayude chila moolyangalkku, "dii" ("jeey", "keey") ≤ "dii" ("keey", "jeey").
invezhs table inv oru akkatthinte gunana vipareethathe prathinidheekarikkunnu, athaayath, "d" ("j", "inv" ("j")) = 0 neey thripthippeduthunna moolyam.
kramaparivarthana pattika p oro akkatthinum akkatthile sthaanathe adisthaanamaakki oru kramaparivarthanam prayogikkunnu. ithu yadhaarthathil aavarthichu prayogikkunna orotta kramappeduthalaanu; i.iii. "p" ("" i "" + "" j "," n "") = "" p "" ("" i "," p "" ("" j "," n "")) ".
werhoff cheksam kanakkukoottal inipparayunna reethiyil nadathunnu
yadhaartha nambar saadhuthayullathaanenkil maathram.
oru check akkam srishtikkunnathinu, a cherkkuka, kanakkukoottal nadatthuka sariyaaya check akkam.
udaaharanagal.
236" ennathinu oru check akkam srishtikkuka
"sii" ennathu 2 aanu, athinaal check akkam "inv" (2) aanu, athaayath 3.
check akkam "2363" saadhookarikkuka
"sii" poojyamaanu, athinaal check sariyaanu.

