MinT - Information on Result #1079788

Information on Result #1079788

Linear OOA(2²²⁹, 4194556, F₂, 4, 13) (dual of [(4194556, 4), 16777995, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁷, 4194301, F₂, 4, 6) (dual of [(4194301, 4), 16777137, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁷, 4194302, F₂, 3, 6) (dual of [(4194302, 3), 12582839, 7]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
linear OOA(2¹⁶², 2097278, F₂, 4, 13) (dual of [(2097278, 4), 8388950, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 127, F₂, 4, 6) (dual of [(127, 4), 487, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁴¹, 2097151, F₂, 4, 13) (dual of [(2097151, 4), 8388463, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(2¹⁴¹, 4194302, F₂, 2, 13) (dual of [(4194302, 2), 8388463, 14]-NRT-code), using
      - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.