MinT - Information on Result #661589

Information on Result #661589

Linear OA(8¹²⁷, 136, F₈, 94) (dual of [136, 9, 95]-code), using juxtaposition based on

linear OA(8⁵⁶, 65, F₈, 46) (dual of [65, 9, 47]-code), using
- the BCH-code C(I) with length 65Â | 8⁴âˆ’1, defining interval IÂ =Â {5,12,19,…,−5}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 47 [i]
linear OA(8⁶², 71, F₈, 47) (dual of [71, 9, 48]-code), using
- constructionÂ X applied to AG(F,16P) âŠ‚ AG(F,21P) [i] based on
  1. linear OA(8⁵⁸, 64, F₈, 47) (dual of [64, 6, 48]-code), using algebraic-geometric code AG(F,16P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]
  2. linear OA(8⁵⁵, 64, F₈, 42) (dual of [64, 9, 43]-code), using algebraic-geometric code AG(F,21P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OA(8⁴, 7, F₈, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,8)), using
    - discarding factors / shortening the dual code based on linear OA(8⁴, 8, F₈, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
      - Reedâ€“Solomon code RS(4,8) [i]

Mode: Constructive and linear.

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