MinT - Information on Result #1068687

Information on Result #1068687

Linear OOA(81²⁹, 1681, F₈₁, 4, 12) (dual of [(1681, 4), 6695, 13]-NRT-code), using OOA 2-folding based on linear OOA(81²⁹, 3362, F₈₁, 2, 12) (dual of [(3362, 2), 6695, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81²⁹, 3363, F₈₁, 2, 12) (dual of [(3363, 2), 6697, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁶, 82, F₈₁, 2, 6) (dual of [(82, 2), 158, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;158,81) [i]
  2. linear OOA(81²³, 3281, F₈₁, 2, 12) (dual of [(3281, 2), 6539, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81²³, 6562, F₈₁, 12) (dual of [6562, 6539, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(81²³, 6563, F₈₁, 12) (dual of [6563, 6540, 13]-code), using
        constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(81²³, 6561, F₈₁, 12) (dual of [6561, 6538, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(81²¹, 6561, F₈₁, 11) (dual of [6561, 6540, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.