MediaWiki API result

{
    "batchcomplete": "",
    "continue": {
        "gapcontinue": "Rekl\u00e1mszociol\u00f3gia",
        "continue": "gapcontinue||"
    },
    "warnings": {
        "main": {
            "*": "Subscribe to the mediawiki-api-announce mailing list at <https://lists.wikimedia.org/mailman/listinfo/mediawiki-api-announce> for notice of API deprecations and breaking changes."
        },
        "revisions": {
            "*": "Because \"rvslots\" was not specified, a legacy format has been used for the output. This format is deprecated, and in the future the new format will always be used."
        }
    },
    "query": {
        "pages": {
            "23737": {
                "pageid": 23737,
                "ns": 0,
                "title": "Reed-Solomon k\u00f3d",
                "revisions": [
                    {
                        "contentformat": "text/x-wiki",
                        "contentmodel": "wikitext",
                        "*": "{{GlobalTemplate|Infoalap|KodElmZHReedSolKod}}\n\n__TOC__\n\n==Konstrukci\u00f3==\n* <math>\\overline{u}= (u_0, u_1,\\ldots , u_{n-1}) \\quad u_i \\in GF(q)</math>\n* <math>u(x)=u_0x+u_1x+ \\ldots+ u_{n-1}x^{k-1} \\quad deg(u(x))=k-1</math>\n* <math>\\alpha</math> a legkisebb primit\u00edv elem <math>GF(q)</math>-ban (rendje <math>q-1</math>) \n* <math>n=q-1</math> (nem r\u00f6vid\u00edtett R-S k\u00f3d)\n* <math>c_i=u(x)|_{x=\\alpha^i} =u_0+u_1 \\alpha^i+u_2(\\alpha^i)^2+ \\ldots+ u_{k-1}(\\alpha^i)^{k-1}</math>\n* <math>\\overline{c}^T= \\left(\\begin{array}{c} \n\tc_0 \\\\ \n\tc_1 \\\\ \n\t\\vdots \\\\\n\tc_{k-1}\n\t\\end{array} \n\t\\right)</math>\n* <math>\\overline{c}=\\overline{u}\\overline{\\overline{G}}</math>\n* <math>\\overline{\\overline{G}}_{k \\times n}=\n\t\\left( \n\t\\begin{array}{ccccc} \n\t1 & 1  & 1 & \\cdots & 1 \\\\ \n\t1 & \\alpha & \\alpha^2 & \\cdots & \\alpha^{n-1} \\\\\n\t1 & \\alpha^2 & \\alpha^4 & \\cdots & \\alpha^{2(n-1)} \\\\\n\t\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n\t1 & \\alpha^{k-1} & \\alpha^{2(k-1)} & \\cdots & \\alpha^{(k-1)(n-1)}\n\t\\end{array} \n\t\\right)</math> gener\u00e1torm\u00e1trix\n\n==Alternat\u00edv konstrukci\u00f3==\n* <math>\\overline{c}= (c_0, c_1,\\ldots , c_{n-1})</math>\n* <math>c(x)=c_0x+c_1x+ \\ldots+ c_{n-1}x^{k-1}</math>\n* <math>c(x)|_{x=\\alpha^i} =c_0+c_1 \\alpha^i+c_2(\\alpha^i)^2+ \\ldots+ c_{k-1}(\\alpha^i)^{i(n-1)}, \\quad i=1, 2, \\ldots, n-k</math>\n* <math>\\overline{\\overline{H}}^T\\overline{c}^T=0</math>\n* <math>\\overline{\\overline{H}}_{(n-k) \\times n}=\n\t\\left( \n\t\\begin{array}{ccccc} \n\t1 & \\alpha & \\alpha^2 & \\cdots & \\alpha^{n-1} \\\\ \n\t1 & \\alpha^2 & \\alpha^4 & \\cdots & \\alpha^{2(n-1)} \\\\\n\t\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n\t1 & \\alpha^{n-k} & \\alpha^{2(n-k)} & \\cdots & \\alpha^{(k-1)(n-k)}\n\t\\end{array} \n\t\\right)</math> parit\u00e1sellen\u0151rz\u0151-m\u00e1trix\n\n\n==\u00c1ltal\u00e1nos m\u00f3dszer G \u00e9s H gyors fel\u00edr\u00e1s\u00e1ra==\n\n==K\u00f3dol\u00e1s==\n# <math>\\overline{c}=\\overline{u} \\overline{\\overline{G}}</math>\n* <math>\\overline{u}</math> az \u00fczenet \n* <math>\\overline{\\overline{G}}_{k \\times n}</math> a gener\u00e1torm\u00e1trix\n\n==Dek\u00f3dol\u00e1s==\n\t1.szindr\u00f3mavektor kisz\u00e1m\u00edt\u00e1sa: <math>\\overline{s}=\\overline{v} \\overline{\\overline{H}}</math> \n* <math>\\overline{v}=\\overline{c}+\\overline{e}</math> a vett vektor\n* <math>\\overline{e}</math> a hibavektor\n* <math>\\overline{\\overline{H}}_{(n-k) \\times n}</math> a parit\u00e1sellen\u0151rz\u0151-m\u00e1trix\n# detekci\u00f3 PGZ-algoritmussal\n# lev\u00e1g\u00e1s\n# szorz\u00e1s az inverzm\u00e1trixszal <math>\\overline{u}=\\overline{\\overline{G}}_{k \\times k}^{-1} \\overline{c}</math>\n\n==PGZ-algoritmus ==\n* Peterson-Gorenstein-Zierler\n* \u00e1bra kellene\n===Az algoritmus l\u00e9p\u00e9sei===\n\t\n# <math>\\overline{\\overline{U}}_{r \\times r}=\n\t\\left( \n\t\\begin{array}{cccc} \n\ts_1 & s_1 & \\cdots & s_r \\\\ \n\ts_2 & s_3 & \\cdots & s_{r+1} \\\\\n\t\\vdots & \\vdots & \\ddots & \\vdots \\\\\n\ts_r & s_{r+1} & \\cdots & s_{2r-1} \\\\\n\t\\end{array} \n\t\\right)</math> m\u00e1trixb\u00f3l kell kiv\u00e1lasztani a legnagyobb olyan <math>t \\times t</math> t\u00edpus\u00fa alm\u00e1trixot, amelyre <math>det(\\overline{\\overline{U}}_{t \\times t})\\neq 0</math> modulo n.\n# <math>\\overline{\\overline{U}}_{t \\times t}\\overline{L}=\\overline{V}</math>, ahol <math>\\overline{V}=\\left(\\begin{array}{c} \n\t-s_{t+1} \\\\ \n\t-s_{t+2} \\\\ \n\t\\vdots \\\\\n\t-s_{2t}\n\t\\end{array} \n\t\\right)</math> \u00e9s <math>\\overline{L}=\\left(\\begin{array}{c} \n\tL_{t} \\\\ \n\tL_{t-1} \\\\ \n\t\\vdots \\\\\n\tL_1\n\t\\end{array} \n\t\\right)</math>.\n\tEzt a line\u00e1ris egyenletrendszert modulo n megoldva kapjuk <math> L_1, L_2,\\ldots , L_t</math> \u00e9rt\u00e9keket.\n# <math>L(x)=1+L_1x+L_2x^2+\\ldots +L_tx^t</math> egyenlet gy\u00f6kei adj\u00e1k  <math> X_1^{-1}, X_2^{-1},\\ldots , X_t^{-1}</math> \u00e9rt\u00e9keket, melyeknek ki kell sz\u00e1molni a multiplikat\u00edv inverz\u00e9t modulo n, \u00edgy kapjuk <math> X_1, X_2,\\ldots , X_t</math> \u00e9rt\u00e9keket.\n# Az el\u0151z\u0151 l\u00e9p\u00e9sben kapott <math>X_j</math> \u00e9rt\u00e9kek <math>\\alpha</math> alap\u00fa logarimtus\u00e1t modulo n v\u00e9ve kapjuk a <math>i_j</math>hibahelyeket: <math>\\log_\\alpha X_j=i_j</math>. (A logaritmus sz\u00e1m\u00edt\u00e1shoz fel kell \u00edrni <math>\\alpha</math> hatv\u00e1nyait modulo n.)\n# <math>\\overline{\\overline{A}}_{t \\times t}\\overline{Y}=\\overline{s}</math>, ahol <math>\\overline{\\overline{A}}_{t \\times t}=\\left( \n\t\\begin{array}{cccc} \n\tX_1 & X_2 & \\cdots & X_t \\\\ \n\tX_1^2 & X_2^2 & \\cdots & X_t^2 \\\\\n\t\\vdots & \\vdots & \\ddots & \\vdots \\\\\n\tX_1^t & X_2^t & \\cdots & X_t^t \\\\\n\t\\end{array} \n\t\\right)</math> \u00e9s <math>\\overline{Y}=\\left(\\begin{array}{c} \n\tY_1 \\\\ \n\tY_2 \\\\ \n\t\\vdots \\\\\n\tY_t\n\t\\end{array} \n\t\\right)</math> Ezt a line\u00e1ris egyenletrendszert megoldva kapjuk <math> Y_1, Y_2,\\ldots , Y_t</math> \u00e9rt\u00e9keket. Ezek az <math>Y_j</math> hiba\u00e9rt\u00e9keket.\n\n==Reed-Solomon k\u00f3dok ciklikus gener\u00e1l\u00e1sa==\n\n==Reed-Solomon k\u00f3dok \"gyors\u00edt\u00e1sa\" -- spektr\u00e1lis k\u00f3dol\u00e1s==\n \n==P\u00e9ld\u00e1k==\n\n* p\u00e9lda\n\n-- [[AdamO|adamo]] - 2006.05.01.\n-- [[RebeliSzaboTamas]] - 2008.01.21.\n\n\n[[Category:Infoalap]]"
                    }
                ]
            },
            "25393": {
                "pageid": 25393,
                "ns": 0,
                "title": "Rekl\u00e1mkamp\u00e1ny anal\u00edzis",
                "revisions": [
                    {
                        "contentformat": "text/x-wiki",
                        "contentmodel": "wikitext",
                        "*": "{{GlobalTemplate|Infoszak|InfoMenAnalizis}}\n\n\n__TOC__\n\n==N\u00e9gyl\u00e9p\u00e9ses modellez\u00e9s==\n==Dimezi\u00f3k csoportos\u00edt\u00e1sa ==\n==Eredm\u00e9ny==\n\n\u00c1bra...\n\n-- [[AdamO|adamo]] - 2007.11.26.\n\n\n[[Category:Infoszak]]"
                    }
                ]
            }
        }
    }
}