MinT - Information on Result #1234969

Information on Result #1234969

Linear OOA(2¹⁷⁷, 2101245, F₂, 4, 12) (dual of [(2101245, 4), 8404803, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁷, 4094, F₂, 4, 6) (dual of [(4094, 4), 16339, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (31, 37, 4094)-net over F₂, using
  - 1 times m-reduction [i] based on digital (31, 38, 4094)-net over F₂, using
    - net defined by OOA [i] based on linear OOA(2³⁸, 4094, F₂, 7, 7) (dual of [(4094, 7), 28620, 8]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(2³⁸, 4095, F₂, 3, 7) (dual of [(4095, 3), 12247, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
linear OOA(2¹⁴⁰, 2097151, F₂, 4, 12) (dual of [(2097151, 4), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 4194302, F₂, 2, 12) (dual of [(4194302, 2), 8388464, 13]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.