MinT - Information on Result #1018585

Information on Result #1018585

Linear OOA(81⁶⁷, 5599046, F₈₁, 3, 11) (dual of [(5599046, 3), 16797071, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁷, 4194301, F₈₁, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(81¹⁷, large, F₈₁, 5) (dual of [large, large−17, 6]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
linear OOA(81⁵⁰, 2799523, F₈₁, 3, 11) (dual of [(2799523, 3), 8398519, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁹, 3322, F₈₁, 3, 5) (dual of [(3322, 3), 9957, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(81², 82, F₈₁, 3, 2) (dual of [(82, 3), 244, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;244,81) [i]
      2. linear OOA(81⁷, 3240, F₈₁, 3, 5) (dual of [(3240, 3), 9713, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(81⁴¹, 2796201, F₈₁, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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.