MinT - Information on Result #1018510

Information on Result #1018510

Linear OOA(81⁵², 5598882, F₈₁, 3, 9) (dual of [(5598882, 3), 16796594, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹³, 4194301, F₈₁, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(81¹³, 8388602, F₈₁, 4) (dual of [8388602, 8388589, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹³, large, F₈₁, 4) (dual of [large, large−13, 5]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
linear OOA(81³⁹, 2799441, F₈₁, 3, 9) (dual of [(2799441, 3), 8398284, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁶, 3240, F₈₁, 3, 4) (dual of [(3240, 3), 9714, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(81⁶, 6480, F₈₁, 4) (dual of [6480, 6474, 5]-code), using
      - 1 times truncation [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(81³³, 2796201, F₈₁, 3, 9) (dual of [(2796201, 3), 8388570, 10]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81³³, large, F₈₁, 9) (dual of [large, large−33, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

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