MinT - Information on Result #1079440

Information on Result #1079440

Linear OOA(2¹⁶⁷, 4194310, F₂, 4, 10) (dual of [(4194310, 4), 16777073, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁶, 4194305, F₂, 4, 5) (dual of [(4194305, 4), 16777174, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (41, 46, 4194305)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹²¹, 2097155, F₂, 4, 10) (dual of [(2097155, 4), 8388499, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁶, 5, F₂, 4, 5) (dual of [(5, 4), 14, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,14P) [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(2¹¹⁵, 2097150, F₂, 4, 10) (dual of [(2097150, 4), 8388485, 11]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹¹⁵, 8388600, F₂, 10) (dual of [8388600, 8388485, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹¹⁵, large, F₂, 10) (dual of [large, large−115, 11]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

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