MinT - Information on Result #664233

Information on Result #664233

Linear OA(9⁹¹, 763, F₉, 27) (dual of [763, 672, 28]-code), using (u,Â u+v)-construction based on

linear OA(9¹⁹, 35, F₉, 13) (dual of [35, 16, 14]-code), using
- constructionÂ X applied to AG(F,9P) âŠ‚ AG(F,10P) [i] based on
  1. linear OA(9¹⁸, 32, F₉, 13) (dual of [32, 14, 14]-code), using algebraic-geometric code AG(F,9P) with degPÂ =Â 2 [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using a function field by SÃ©mirat [i]
  2. linear OA(9¹⁶, 32, F₉, 11) (dual of [32, 16, 12]-code), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32 (see above)
  3. linear OA(9¹, 3, F₉, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(9⁷², 728, F₉, 27) (dual of [728, 656, 28]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728Â = 9³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]

Mode: Constructive and linear.

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