MinT - Information on Result #1017303

Information on Result #1017303

Linear OOA(49⁵², 1921652, F₄₉, 3, 12) (dual of [(1921652, 3), 5764904, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49⁷, 51, F₄₉, 3, 6) (dual of [(51, 3), 146, 7]-NRT-code), using
- extracting embedded OOA [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(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
      1. 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]
      2. 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]
      3. 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.