MinT - Information on Result #899726

Information on Result #899726

Linear OOA(25⁷⁸, 195383, F₂₅, 2, 17) (dual of [(195383, 2), 390688, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹², 66, F₂₅, 2, 8) (dual of [(66, 2), 120, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,123P) [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(25⁶⁶, 195317, F₂₅, 2, 17) (dual of [(195317, 2), 390568, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁶⁶, 390634, F₂₅, 17) (dual of [390634, 390568, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁶⁶, 390635, F₂₅, 17) (dual of [390635, 390569, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(25⁶⁵, 390626, F₂₅, 17) (dual of [390626, 390561, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. 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]
      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, using
        parity-check code [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(25⁷⁸, 48845, F₂₅, 18, 17) (dual of [(48845, 18), 879132, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row