MinT - Information on Result #1189426

Information on Result #1189426

Digital (95, 117, 1425)-net over F₅, using net defined by OOA based on linear OOA(5¹¹⁷, 1425, F₅, 22, 22) (dual of [(1425, 22), 31233, 23]-NRT-code), using

OA 11-folding and stacking [i] based on linear OA(5¹¹⁷, 15675, F₅, 22) (dual of [15675, 15558, 23]-code), using
- constructionÂ X applied to C_e(21) âŠ‚ C_e(13) [i] based on
  1. linear OA(5¹⁰³, 15625, F₅, 22) (dual of [15625, 15522, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  2. linear OA(5⁶⁷, 15625, F₅, 14) (dual of [15625, 15558, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  3. linear OA(5¹⁴, 50, F₅, 7) (dual of [50, 36, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(5¹⁴, 52, F₅, 7) (dual of [52, 38, 8]-code), using
      - trace code [i] based on linear OA(25⁷, 26, F₂₅, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
        extended Reedâ€“Solomon code RS_e(19,25) [i]
        the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
        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]
        algebraic-geometric code AG(F,6P) with degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.