MinT - Information on Result #1191104

Information on Result #1191104

Digital (27, 34, 10932)-net over F₈, using net defined by OOA based on linear OOA(8³⁴, 10932, F₈, 9, 7) (dual of [(10932, 9), 98354, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8³⁴, 10933, F₈, 3, 7) (dual of [(10933, 3), 32765, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8³, 9, F₈, 3, 3) (dual of [(9, 3), 24, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;24,8) [i]
  2. linear OOA(8³¹, 10924, F₈, 3, 7) (dual of [(10924, 3), 32741, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8³¹, 32772, F₈, 7) (dual of [32772, 32741, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(8³¹, 32773, F₈, 7) (dual of [32773, 32742, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(8³¹, 32768, F₈, 7) (dual of [32768, 32737, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(8²⁶, 32768, F₈, 6) (dual of [32768, 32742, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.