MinT - Information on Result #1196417

Information on Result #1196417

Linear OOA(25⁶⁶, 55809, F₂₅, 15, 15) (dual of [(55809, 15), 837069, 16]-NRT-code), using OOA 7-folding and stacking with additional row based on linear OA(25⁶⁶, 390664, F₂₅, 15) (dual of [390664, 390598, 16]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(25⁸, 29, F₂₅, 7) (dual of [29, 21, 8]-code), using
  - constructionÂ X applied to AG(F,9P) âŠ‚ AG(F,10P) [i] based on
    1. linear OA(25⁷, 26, F₂₅, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using algebraic-geometric code AG(F,9P) with 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]
    2. linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
    3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 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]
2. linear OA(25⁵⁸, 390635, F₂₅, 15) (dual of [390635, 390577, 16]-code), using
  - constructionÂ X applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(25⁵⁷, 390626, F₂₅, 15) (dual of [390626, 390569, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    2. linear OA(25⁴⁹, 390626, F₂₅, 13) (dual of [390626, 390577, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    3. linear OA(25¹, 9, F₂₅, 1) (dual of [9, 8, 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 (see above)

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (51, 66, 55809)-net over F₂₅	[i]		Net Defined by OOA