MinT - Information on Result #1008941

Information on Result #1008941

Linear OOA(8¹⁶⁴, 8388602, F₈, 3, 15) (dual of [(8388602, 3), 25165642, 16]-NRT-code), using trace code based on linear OOA(64⁸², 4194301, F₆₄, 3, 15) (dual of [(4194301, 3), 12582821, 16]-NRT-code), using

OOA 2-folding [i] based on linear OOA(64⁸², 8388602, F₆₄, 2, 15) (dual of [(8388602, 2), 16777122, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64²⁵, 4194301, F₆₄, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(64²⁵, 8388602, F₆₄, 7) (dual of [8388602, 8388577, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  2. linear OOA(64⁵⁷, 4194301, F₆₄, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(64⁵⁷, 8388602, F₆₄, 15) (dual of [8388602, 8388545, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.