MinT - Information on Result #732996

Information on Result #732996

Linear OA(25³⁴, 390661, F₂₅, 8) (dual of [390661, 390627, 9]-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(25³⁰, 390635, F₂₅, 8) (dual of [390635, 390605, 9]-code), using
- constructionÂ X4 applied to C_e(7) âŠ‚ C_e(5) [i] based on
  1. linear OA(25²⁹, 390625, F₂₅, 8) (dual of [390625, 390596, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  2. linear OA(25²¹, 390625, F₂₅, 6) (dual of [390625, 390604, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(25³⁴, 195330, F₂₅, 2, 8) (dual of [(195330, 2), 390626, 9]-NRT-code)	[i]		OOA Folding