MinT - Information on Result #1013902

Information on Result #1013902

Linear OOA(7¹⁰⁹, 3843406, F₇, 3, 12) (dual of [(3843406, 3), 11530109, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹⁹, 204, F₇, 3, 6) (dual of [(204, 3), 593, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁵, 132, F₇, 3, 3) (dual of [(132, 3), 391, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(7⁵, 132, F₇, 2, 3) (dual of [(132, 2), 259, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁵, 132, F₇, 3) (dual of [132, 127, 4]-code or 132-cap in PG(4,7)), using
        caps completed using a computer search [i]
  2. linear OOA(7¹⁴, 102, F₇, 3, 6) (dual of [(102, 3), 292, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 14, 102)-net over F₇, using
      - trace code for nets [i] based on digital (1, 7, 51)-net over F₄₉, using
        net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
linear OOA(7⁹⁰, 3843202, F₇, 3, 12) (dual of [(3843202, 3), 11529516, 13]-NRT-code), using
- trace code [i] based on linear OOA(49⁴⁵, 1921601, F₄₉, 3, 12) (dual of [(1921601, 3), 5764758, 13]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(49⁴⁵, 5764803, F₄₉, 12) (dual of [5764803, 5764758, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(49⁴⁵, 5764805, F₄₉, 12) (dual of [5764805, 5764760, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(49⁴⁵, 5764801, F₄₉, 12) (dual of [5764801, 5764756, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(49⁴¹, 5764801, F₄₉, 11) (dual of [5764801, 5764760, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.