MinT - Information on Result #1192620

Information on Result #1192620

Digital (138, 162, 174768)-net over F₈, using net defined by OOA based on linear OOA(8¹⁶², 174768, F₈, 27, 24) (dual of [(174768, 27), 4718574, 25]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(8¹⁶², 699073, F₈, 3, 24) (dual of [(699073, 3), 2097057, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹⁶², 699074, F₈, 3, 24) (dual of [(699074, 3), 2097060, 25]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(8¹⁵, 24, F₈, 3, 12) (dual of [(24, 3), 57, 13]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,59P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
        the Klein quartic over F₈ [i]
    2. linear OOA(8¹⁴⁷, 699050, F₈, 3, 24) (dual of [(699050, 3), 2097003, 25]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(8¹⁴⁷, 2097150, F₈, 24) (dual of [2097150, 2097003, 25]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹⁴⁷, 2097151, F₈, 24) (dual of [2097151, 2097004, 25]-code), using
        1 times truncation [i] based on linear OA(8¹⁴⁸, 2097152, F₈, 25) (dual of [2097152, 2097004, 26]-code), using
        an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]

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.