MinT - Information on Result #1082431

Information on Result #1082431

Linear OOA(81⁶⁴, 4194500, F₈₁, 4, 11) (dual of [(4194500, 4), 16777936, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁷, 4194301, F₈₁, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(81¹⁷, large, F₈₁, 5) (dual of [large, large−17, 6]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
linear OOA(81⁴⁷, 2097250, F₈₁, 4, 11) (dual of [(2097250, 4), 8388953, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁶, 100, F₈₁, 4, 5) (dual of [(100, 4), 394, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,394P) [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(81⁴¹, 2097150, F₈₁, 4, 11) (dual of [(2097150, 4), 8388559, 12]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(81⁴¹, 8388600, F₈₁, 11) (dual of [8388600, 8388559, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

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