MinT - Information on Result #670294

Information on Result #670294

Linear OA(81⁶⁹, 6736, F₈₁, 25) (dual of [6736, 6667, 26]-code), using (u,Â u+v)-construction based on

linear OA(81²⁰, 174, F₈₁, 12) (dual of [174, 154, 13]-code), using
- constructionÂ X applied to AG(F,158P) âŠ‚ AG(F,160P) [i] based on
  1. linear OA(81¹⁹, 171, F₈₁, 12) (dual of [171, 152, 13]-code), using algebraic-geometric code AG(F,158P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]
  2. linear OA(81¹⁷, 171, F₈₁, 10) (dual of [171, 154, 11]-code), using algebraic-geometric code AG(F,160P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (see above)
  3. linear OA(81¹, 3, F₈₁, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(81⁴⁹, 6562, F₈₁, 25) (dual of [6562, 6513, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Mode: Constructive and linear.

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