MinT - Information on Result #1022121

Information on Result #1022121

Linear OOA(49⁵³, 951, F₄₉, 3, 19) (dual of [(951, 3), 2800, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49¹⁶, 150, F₄₉, 3, 9) (dual of [(150, 3), 434, 10]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(49³, 50, F₄₉, 3, 3) (dual of [(50, 3), 147, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;147,49) [i]
  2. linear OOA(49⁴, 50, F₄₉, 3, 4) (dual of [(50, 3), 146, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;146,49) [i]
  3. linear OOA(49⁹, 50, F₄₉, 3, 9) (dual of [(50, 3), 141, 10]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;141,49) [i]
linear OOA(49³⁷, 801, F₄₉, 3, 19) (dual of [(801, 3), 2366, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(49³⁷, 2403, F₄₉, 19) (dual of [2403, 2366, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
    1. linear OA(49³⁷, 2401, F₄₉, 19) (dual of [2401, 2364, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(49³⁵, 2401, F₄₉, 18) (dual of [2401, 2366, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.