MinT - Information on Result #1131505

Information on Result #1131505

Linear OOA(2²³⁷, 1399465, F₂, 6, 17) (dual of [(1399465, 6), 8396553, 18]-NRT-code), using OOA 3-folding based on linear OOA(2²³⁷, 4198395, F₂, 2, 17) (dual of [(4198395, 2), 8396553, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁷, 4198397, F₂, 2, 17) (dual of [(4198397, 2), 8396557, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵², 4096, F₂, 2, 8) (dual of [(4096, 2), 8140, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2⁵², 8192, F₂, 8) (dual of [8192, 8140, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁵³, 8193, F₂, 9) (dual of [8193, 8140, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OOA(2¹⁸⁵, 4194301, F₂, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁸⁵, 8388602, F₂, 17) (dual of [8388602, 8388417, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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.