MinT - Information on Result #1190206

Information on Result #1190206

Digital (71, 82, 1921601)-net over F₇, using net defined by OOA based on linear OOA(7⁸², 1921601, F₇, 14, 11) (dual of [(1921601, 14), 26902332, 12]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(7⁸², 5764804, F₇, 2, 11) (dual of [(5764804, 2), 11529526, 12]-NRT-code), using
- trace code [i] based on linear OOA(49⁴¹, 2882402, F₄₉, 2, 11) (dual of [(2882402, 2), 5764763, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(49⁴¹, 5764804, F₄₉, 11) (dual of [5764804, 5764763, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(49⁴¹, 5764805, F₄₉, 11) (dual of [5764805, 5764764, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        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(49³⁷, 5764801, F₄₉, 10) (dual of [5764801, 5764764, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.