MinT - Information on Result #663745

Information on Result #663745

Linear OA(8¹³², 32805, F₈, 26) (dual of [32805, 32673, 27]-code), using (u,Â u+v)-construction based on

linear OA(8²¹, 37, F₈, 13) (dual of [37, 16, 14]-code), using
- constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,11P) [i] based on
  1. linear OA(8²⁰, 34, F₈, 13) (dual of [34, 14, 14]-code), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using a function field by SÃ©mirat [i]
  2. linear OA(8¹⁸, 34, F₈, 11) (dual of [34, 16, 12]-code), using algebraic-geometric code AG(F,11P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34 (see above)
  3. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(8¹¹¹, 32768, F₈, 26) (dual of [32768, 32657, 27]-code), using
- an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Mode: Constructive and linear.

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