MinT - Information on Result #1117147

Information on Result #1117147

Linear OOA(3¹⁵⁴, 4194308, F₃, 5, 10) (dual of [(4194308, 5), 20971386, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶, 7, F₃, 5, 5) (dual of [(7, 5), 29, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁶, 7, F₃, 4, 5) (dual of [(7, 4), 22, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,22P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁴⁸, 4194301, F₃, 5, 10) (dual of [(4194301, 5), 20971357, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁴⁸, 8388602, F₃, 3, 10) (dual of [(8388602, 3), 25165658, 11]-NRT-code), using
  - trace code [i] based on linear OOA(9⁷⁴, 4194301, F₉, 3, 10) (dual of [(4194301, 3), 12582829, 11]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(9⁷⁴, 8388602, F₉, 2, 10) (dual of [(8388602, 2), 16777130, 11]-NRT-code), using
      - trace code [i] based on linear OOA(81³⁷, 4194301, F₈₁, 2, 10) (dual of [(4194301, 2), 8388565, 11]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81³⁷, 8388602, F₈₁, 10) (dual of [8388602, 8388565, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

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