MinT - Information on Result #666088

Information on Result #666088

Linear OA(25⁸⁷, 15654, F₂₅, 26) (dual of [15654, 15567, 27]-code), using (u,Â u+v)-construction based on

linear OA(25¹⁴, 29, F₂₅, 13) (dual of [29, 15, 14]-code), using
- constructionÂ X applied to AG(F,6P) âŠ‚ AG(F,7P) [i] based on
  1. 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, using the rational function field F₂₅(x) [i]
  2. linear OA(25¹¹, 26, F₂₅, 11) (dual of [26, 15, 12]-code or 26-arc in PG(10,25)), using algebraic-geometric code AG(F,7P) 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(25⁷³, 15625, F₂₅, 26) (dual of [15625, 15552, 27]-code), using
- an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’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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