MinT - Information on Result #1068552

Information on Result #1068552

Linear OOA(81¹⁹, 1681, F₈₁, 4, 8) (dual of [(1681, 4), 6705, 9]-NRT-code), using OOA 2-folding based on linear OOA(81¹⁹, 3362, F₈₁, 2, 8) (dual of [(3362, 2), 6705, 9]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81¹⁹, 3363, F₈₁, 2, 8) (dual of [(3363, 2), 6707, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁴, 82, F₈₁, 2, 4) (dual of [(82, 2), 160, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;160,81) [i]
  2. linear OOA(81¹⁵, 3281, F₈₁, 2, 8) (dual of [(3281, 2), 6547, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81¹⁵, 6562, F₈₁, 8) (dual of [6562, 6547, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(81¹⁵, 6563, F₈₁, 8) (dual of [6563, 6548, 9]-code), using
        constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        linear OA(81¹⁵, 6561, F₈₁, 8) (dual of [6561, 6546, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(81¹³, 6561, F₈₁, 7) (dual of [6561, 6548, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.