MinT - Information on Result #1082816

Information on Result #1082816

Linear OOA(81⁷⁵, 1856, F₈₁, 4, 27) (dual of [(1856, 4), 7349, 28]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81²², 216, F₈₁, 4, 13) (dual of [(216, 4), 842, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁷, 100, F₈₁, 4, 6) (dual of [(100, 4), 393, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,393P) [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, 116, F₈₁, 4, 13) (dual of [(116, 4), 449, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,450P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]
linear OOA(81⁵³, 1640, F₈₁, 4, 27) (dual of [(1640, 4), 6507, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁵³, 6560, F₈₁, 27) (dual of [6560, 6507, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵³, 6561, F₈₁, 27) (dual of [6561, 6508, 28]-code), using
    - an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]

Mode: Constructive and linear.

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