MinT - Information on Result #903261

Information on Result #903261

Linear OOA(49⁵⁴, 2882502, F₄₉, 2, 12) (dual of [(2882502, 2), 5764950, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49⁹, 100, F₄₉, 2, 6) (dual of [(100, 2), 191, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49³, 50, F₄₉, 2, 3) (dual of [(50, 2), 97, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;97,49) [i]
  2. linear OOA(49⁶, 50, F₄₉, 2, 6) (dual of [(50, 2), 94, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;94,49) [i]
linear OOA(49⁴⁵, 2882402, F₄₉, 2, 12) (dual of [(2882402, 2), 5764759, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49⁴⁵, 5764804, F₄₉, 12) (dual of [5764804, 5764759, 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.