MinT - Information on Result #1013654

Information on Result #1013654

Linear OOA(7³⁷, 5764861, F₇, 3, 5) (dual of [(5764861, 3), 17294546, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7³, 57, F₇, 3, 2) (dual of [(57, 3), 168, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(7³, 57, F₇, 2, 2) (dual of [(57, 2), 111, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(7³, 57, F₇, 2) (dual of [57, 54, 3]-code), using
    - Hamming code H(3,7) [i]
linear OOA(7³⁴, 5764804, F₇, 3, 5) (dual of [(5764804, 3), 17294378, 6]-NRT-code), using
- trace code [i] based on linear OOA(49¹⁷, 2882402, F₄₉, 3, 5) (dual of [(2882402, 3), 8647189, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(49¹⁷, 5764805, F₄₉, 5) (dual of [5764805, 5764788, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(49¹⁷, 5764801, F₄₉, 5) (dual of [5764801, 5764784, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.