MinT - Information on Result #732986

Information on Result #732986

Linear OA(25³⁸, 390662, F₂₅, 9) (dual of [390662, 390624, 10]-code), using (u,Â u+v)-construction based on

linear OA(25⁴, 26, F₂₅, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
- extended Reedâ€“Solomon code RS_e(22,25) [i]
- algebraic-geometric code AG(F, Q+9P) 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]
- algebraic-geometric code AG(F,7P) with degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
linear OA(25³⁴, 390636, F₂₅, 9) (dual of [390636, 390602, 10]-code), using
- constructionÂ X4 applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
  1. linear OA(25³³, 390626, F₂₅, 9) (dual of [390626, 390593, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OA(25²⁵, 390626, F₂₅, 7) (dual of [390626, 390601, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  3. linear OA(25⁹, 10, F₂₅, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,25)), using
    - dual of repetition code with length 10 [i]
  4. linear OA(25¹, 10, F₂₅, 1) (dual of [10, 9, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, 25, F₂₅, 1) (dual of [25, 24, 2]-code), using
      - Reedâ€“Solomon code RS(24,25) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(25³⁸, 195331, F₂₅, 2, 9) (dual of [(195331, 2), 390624, 10]-NRT-code)	[i]		OOA Folding