MinT - Information on Result #1082827

Information on Result #1082827

Linear OOA(81⁷⁸, 1840, F₈₁, 4, 28) (dual of [(1840, 4), 7282, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81²³, 200, F₈₁, 4, 14) (dual of [(200, 4), 777, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁸, 100, F₈₁, 4, 7) (dual of [(100, 4), 392, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,392P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(81¹⁵, 100, F₈₁, 4, 14) (dual of [(100, 4), 385, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,385P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100 (see above)
linear OOA(81⁵⁵, 1640, F₈₁, 4, 28) (dual of [(1640, 4), 6505, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁵⁵, 6560, F₈₁, 28) (dual of [6560, 6505, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵⁵, 6561, F₈₁, 28) (dual of [6561, 6506, 29]-code), using
    - an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]

Mode: Constructive and linear.

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