MinT - Information on Result #1831699

Information on Result #1831699

OOA(27⁵⁸, 4197623, S₂₇, 2, 10), using (u,Â u+v)-construction based on

OOA(27¹², 3322, S₂₇, 2, 5), using
- extracting embedded OOA [i] based on (7, 12, 3322)-net in base 27, using
  - base change [i] based on digital (4, 9, 3322)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81⁹, 3322, F₈₁, 5, 5) (dual of [(3322, 5), 16601, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(81⁹, 3322, F₈₁, 4, 5) (dual of [(3322, 4), 13279, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(81², 82, F₈₁, 4, 2) (dual of [(82, 4), 326, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;326,81) [i]
        linear OOA(81⁷, 3240, F₈₁, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(27⁴⁶, 4194301, F₂₇, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁴⁶, 8388602, F₂₇, 10) (dual of [8388602, 8388556, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁴⁶, large, F₂₇, 10) (dual of [large, large−46, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

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