MinT - Information on Result #1068856

Information on Result #1068856

Linear OOA(81⁶⁹, 2097273, F₈₁, 4, 15) (dual of [(2097273, 4), 8389023, 16]-NRT-code), using OOA 2-folding based on linear OOA(81⁶⁹, 4194546, F₈₁, 2, 15) (dual of [(4194546, 2), 8389023, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁶⁹, 4194547, F₈₁, 2, 15) (dual of [(4194547, 2), 8389025, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81¹², 246, F₈₁, 2, 7) (dual of [(246, 2), 480, 8]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;162,81) [i]
      2. linear OOA(81³, 82, F₈₁, 2, 3) (dual of [(82, 2), 161, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;161,81) [i]
      3. linear OOA(81⁷, 82, F₈₁, 2, 7) (dual of [(82, 2), 157, 8]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;157,81) [i]
  2. linear OOA(81⁵⁷, 4194301, F₈₁, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81⁵⁷, 8388602, F₈₁, 15) (dual of [8388602, 8388545, 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.