MinT - Information on Result #1084779

Information on Result #1084779

Linear OOA(81⁷⁵, 4194400, F₈₁, 4, 13) (dual of [(4194400, 4), 16777525, 14]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(81⁵, 100, F₈₁, 4, 4) (dual of [(100, 4), 395, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(81⁵, 100, F₈₁, 3, 4) (dual of [(100, 3), 295, 5]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,295P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]
linear OOA(81²¹, 2097150, F₈₁, 4, 6) (dual of [(2097150, 4), 8388579, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81²¹, 2796201, F₈₁, 4, 6) (dual of [(2796201, 4), 11184783, 7]-NRT-code), using
  - OA 3-folding and stacking [i] based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(81⁴⁹, 2097150, F₈₁, 4, 13) (dual of [(2097150, 4), 8388551, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁴⁹, 8388600, F₈₁, 13) (dual of [8388600, 8388551, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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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