MinT - Information on Result #1082585

Information on Result #1082585

Linear OOA(81⁷¹, 2099338, F₈₁, 4, 15) (dual of [(2099338, 4), 8397281, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁴, 2188, F₈₁, 4, 7) (dual of [(2188, 4), 8738, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(81¹⁴, 6565, F₈₁, 7) (dual of [6565, 6551, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹⁴, 6567, F₈₁, 7) (dual of [6567, 6553, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(81¹³, 6562, F₈₁, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(81⁹, 6562, F₈₁, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(81¹, 5, F₈₁, 1) (dual of [5, 4, 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]
linear OOA(81⁵⁷, 2097150, F₈₁, 4, 15) (dual of [(2097150, 4), 8388543, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁵⁷, 8388600, F₈₁, 15) (dual of [8388600, 8388543, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.