MinT - Information on Result #665993

Information on Result #665993

Linear OA(25¹⁰¹, 15654, F₂₅, 30) (dual of [15654, 15553, 31]-code), using (u,Â u+v)-construction based on

linear OA(25¹⁶, 29, F₂₅, 15) (dual of [29, 13, 16]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,6P) [i] based on
  1. linear OA(25¹⁵, 26, F₂₅, 15) (dual of [26, 11, 16]-code or 26-arc in PG(14,25)), using algebraic-geometric code AG(F,5P) with 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(25¹³, 26, F₂₅, 13) (dual of [26, 13, 14]-code or 26-arc in PG(12,25)), using algebraic-geometric code AG(F,6P) with 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(25⁸⁵, 15625, F₂₅, 30) (dual of [15625, 15540, 31]-code), using
- an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]

Mode: Constructive and linear.

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