MinT - Information on Result #666147

Information on Result #666147

Linear OA(25¹⁰⁶, 390654, F₂₅, 24) (dual of [390654, 390548, 25]-code), using (u,Â u+v)-construction based on

linear OA(25¹³, 29, F₂₅, 12) (dual of [29, 16, 13]-code), using
- constructionÂ X applied to AG(F, Q+5P) âŠ‚ AG(F, Q+6P) [i] based on
  1. linear OA(25¹², 26, F₂₅, 12) (dual of [26, 14, 13]-code or 26-arc in PG(11,25)), using algebraic-geometric code AG(F, Q+5P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
  2. linear OA(25¹⁰, 26, F₂₅, 10) (dual of [26, 16, 11]-code or 26-arc in PG(9,25)), using algebraic-geometric code AG(F, Q+6P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
  3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(25⁹³, 390625, F₂₅, 24) (dual of [390625, 390532, 25]-code), using
- an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Mode: Constructive and linear.

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