MinT - Information on Result #899857

Information on Result #899857

Linear OOA(25⁹³, 195385, F₂₅, 2, 20) (dual of [(195385, 2), 390677, 21]-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(25⁷⁹, 195319, F₂₅, 2, 20) (dual of [(195319, 2), 390559, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁹, 390638, F₂₅, 20) (dual of [390638, 390559, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁷⁹, 390639, F₂₅, 20) (dual of [390639, 390560, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(16) [i] based on
      1. linear OA(25⁷⁷, 390625, F₂₅, 20) (dual of [390625, 390548, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(25⁶⁵, 390625, F₂₅, 17) (dual of [390625, 390560, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.