MinT - Information on Result #903334

Information on Result #903334

Linear OOA(49⁴³, 1301, F₄₉, 2, 16) (dual of [(1301, 2), 2559, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49¹², 100, F₄₉, 2, 8) (dual of [(100, 2), 188, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49⁴, 50, F₄₉, 2, 4) (dual of [(50, 2), 96, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;96,49) [i]
  2. linear OOA(49⁸, 50, F₄₉, 2, 8) (dual of [(50, 2), 92, 9]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;92,49) [i]
linear OOA(49³¹, 1201, F₄₉, 2, 16) (dual of [(1201, 2), 2371, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49³¹, 2402, F₄₉, 16) (dual of [2402, 2371, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(49³¹, 2403, F₄₉, 16) (dual of [2403, 2372, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
      1. linear OA(49³¹, 2401, F₄₉, 16) (dual of [2401, 2370, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(49²⁹, 2401, F₄₉, 15) (dual of [2401, 2372, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      3. linear OA(49⁰, 2, F₄₉, 0) (dual of [2, 2, 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.