MinT - Information on Result #1079647

Information on Result #1079647

Linear OOA(2²¹³, 4194312, F₂, 4, 12) (dual of [(4194312, 4), 16777035, 13]-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(2¹⁴⁶, 2097156, F₂, 4, 12) (dual of [(2097156, 4), 8388478, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁸, 6, F₂, 4, 6) (dual of [(6, 4), 16, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,17P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 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.

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