MinT - Information on Result #3010902

Information on Result #3010902

Linear OOA(2¹⁶¹, 2097277, F₂, 8, 13) (dual of [(2097277, 8), 16778055, 14]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁶⁰, 2097277, F₂, 8, 13) (dual of [(2097277, 8), 16778056, 14]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁶⁰, 2097277, F₂, 4, 13) (dual of [(2097277, 4), 8388948, 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(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 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: 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.