MinT - Information on Result #1014308

Information on Result #1014308

Linear OOA(8⁸¹, 5596507, F₈, 3, 9) (dual of [(5596507, 3), 16789440, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁵, 4105, F₈, 3, 4) (dual of [(4105, 3), 12300, 5]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8³, 73, F₈, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
        Hamming code H(3,8) [i]
  2. linear OOA(8¹², 4032, F₈, 3, 4) (dual of [(4032, 3), 12084, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(8¹², 8064, F₈, 4) (dual of [8064, 8052, 5]-code), using
      - trace code [i] based on linear OA(64⁶, 4032, F₆₄, 4) (dual of [4032, 4026, 5]-code), using
        1 times truncation [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(8⁶⁶, 5592402, F₈, 3, 9) (dual of [(5592402, 3), 16777140, 10]-NRT-code), using
- trace code [i] based on linear OOA(64³³, 2796201, F₆₄, 3, 9) (dual of [(2796201, 3), 8388570, 10]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64³³, large, F₆₄, 9) (dual of [large, large−33, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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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