MinT - Information on Result #1563740

Information on Result #1563740

Linear OOA(49³⁸, 893, F₄₉, 3, 19) (dual of [(893, 3), 2641, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(49³⁸, 893, F₄₉, 2, 19) (dual of [(893, 2), 1748, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(49³⁸, 1203, F₄₉, 2, 19) (dual of [(1203, 2), 2368, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49³⁸, 2406, F₄₉, 19) (dual of [2406, 2368, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(49³⁸, 2407, F₄₉, 19) (dual of [2407, 2369, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(49³⁷, 2402, F₄₉, 19) (dual of [2402, 2365, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402Â | 49⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. 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]
      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: 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(49³⁸, 297, F₄₉, 21, 19) (dual of [(297, 21), 6199, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row