MinT - Information on Result #1079769

Information on Result #1079769

Linear OOA(2²¹¹, 4194305, F₂, 4, 13) (dual of [(4194305, 4), 16777009, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 4, 6) (dual of [(2097150, 4), 8388535, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 6) (dual of [(2097151, 3), 6291388, 7]-NRT-code), using
  - strength reduction [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
linear OOA(2¹⁴⁶, 2097155, F₂, 4, 13) (dual of [(2097155, 4), 8388474, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁷, 5, F₂, 4, 6) (dual of [(5, 4), 13, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,13P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [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: Constructive and linear.

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