MinT - Information on Result #899894

Information on Result #899894

Linear OOA(25⁹⁷, 195385, F₂₅, 2, 21) (dual of [(195385, 2), 390673, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁴, 66, F₂₅, 2, 10) (dual of [(66, 2), 118, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,121P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(25⁸³, 195319, F₂₅, 2, 21) (dual of [(195319, 2), 390555, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁸³, 390638, F₂₅, 21) (dual of [390638, 390555, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁸³, 390639, F₂₅, 21) (dual of [390639, 390556, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(17) [i] based on
      1. linear OA(25⁸¹, 390625, F₂₅, 21) (dual of [390625, 390544, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(25⁶⁹, 390625, F₂₅, 18) (dual of [390625, 390556, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. linear OA(25², 14, F₂₅, 2) (dual of [14, 12, 3]-code or 14-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]

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.