MinT - Information on Result #903358

Information on Result #903358

Linear OOA(49⁴⁶, 1303, F₄₉, 2, 17) (dual of [(1303, 2), 2560, 18]-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(49³⁴, 1203, F₄₉, 2, 17) (dual of [(1203, 2), 2372, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49³⁴, 2406, F₄₉, 17) (dual of [2406, 2372, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(49³⁴, 2407, F₄₉, 17) (dual of [2407, 2373, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(49³³, 2402, F₄₉, 17) (dual of [2402, 2369, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402Â | 49⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. linear OA(49²⁹, 2402, F₄₉, 15) (dual of [2402, 2373, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402Â | 49⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      3. linear OA(49¹, 5, F₄₉, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.