MinT - Information on Result #906736

Information on Result #906736

Linear OOA(25⁵⁵, 7892, F₂₅, 2, 15) (dual of [(7892, 2), 15729, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹², 78, F₂₅, 2, 7) (dual of [(78, 2), 144, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(25², 26, F₂₅, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;50,25) [i]
  2. linear OOA(25³, 26, F₂₅, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;49,25) [i]
  3. linear OOA(25⁷, 26, F₂₅, 2, 7) (dual of [(26, 2), 45, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;45,25) [i]
linear OOA(25⁴³, 7814, F₂₅, 2, 15) (dual of [(7814, 2), 15585, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁴³, 15628, F₂₅, 15) (dual of [15628, 15585, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
    1. linear OA(25⁴³, 15625, F₂₅, 15) (dual of [15625, 15582, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(25⁴⁰, 15625, F₂₅, 14) (dual of [15625, 15585, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(25⁰, 3, F₂₅, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.