MinT - Information on Result #1613805

Information on Result #1613805

Linear OOA(81⁶², 217090, F₈₁, 4, 21) (dual of [(217090, 4), 868298, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(81⁶², 217090, F₈₁, 2, 21) (dual of [(217090, 2), 434118, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁶², 265724, F₈₁, 2, 21) (dual of [(265724, 2), 531386, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁶², 531448, F₈₁, 21) (dual of [531448, 531386, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁶², 531449, F₈₁, 21) (dual of [531449, 531387, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(81⁶¹, 531442, F₈₁, 21) (dual of [531442, 531381, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(81⁵⁵, 531442, F₈₁, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 81⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(81¹, 7, F₈₁, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 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(81⁶², 72363, F₈₁, 28, 21) (dual of [(72363, 28), 2026102, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row