MinT - Information on Result #732654

Information on Result #732654

Linear OA(25⁶³, 701, F₂₅, 23) (dual of [701, 638, 24]-code), using (u,Â u+v)-construction based on

linear OA(25¹⁷, 70, F₂₅, 11) (dual of [70, 53, 12]-code), using
- constructionÂ X applied to AG(F,53P) âŠ‚ AG(F,56P) [i] based on
  1. linear OA(25¹⁵, 65, F₂₅, 11) (dual of [65, 50, 12]-code), using algebraic-geometric code AG(F,53P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(25¹², 65, F₂₅, 8) (dual of [65, 53, 9]-code), using algebraic-geometric code AG(F,56P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
  3. linear OA(25², 5, F₂₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
    - discarding factors / shortening the dual code based on linear OA(25², 25, F₂₅, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
      - Reedâ€“Solomon code RS(23,25) [i]
linear OA(25⁴⁶, 631, F₂₅, 23) (dual of [631, 585, 24]-code), using
- constructionÂ X applied to C([0,11]) âŠ‚ C([0,10]) [i] based on
  1. linear OA(25⁴⁵, 626, F₂₅, 23) (dual of [626, 581, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 626Â | 25⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
  2. linear OA(25⁴¹, 626, F₂₅, 21) (dual of [626, 585, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 626Â | 25⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  3. linear OA(25¹, 5, F₂₅, 1) (dual of [5, 4, 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]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.