MinT - Information on Result #1179644

Information on Result #1179644

Digital (8, 12, 58876)-net over F₄₉, using net defined by OOA based on linear OOA(49¹², 58876, F₄₉, 4, 4) (dual of [(58876, 4), 235492, 5]-NRT-code), using

appending kth column [i] based on linear OOA(49¹², 58876, F₄₉, 3, 4) (dual of [(58876, 3), 176616, 5]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49², 50, F₄₉, 3, 2) (dual of [(50, 3), 148, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;148,49) [i]
  2. linear OOA(49¹⁰, 58826, F₄₉, 3, 4) (dual of [(58826, 3), 176468, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(49¹⁰, 117652, F₄₉, 4) (dual of [117652, 117642, 5]-code), using
      - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(49¹⁰, 117649, F₄₉, 4) (dual of [117649, 117639, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(49⁷, 117649, F₄₉, 3) (dual of [117649, 117642, 4]-code or 117649-cap in PG(6,49)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(49⁰, 3, F₄₉, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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

The following results depend on this result:

	Result		This result only	Method
1	Digital (45, 53, 4267249)-net over F₄₉	[i]		Generalized (u,Â u+v)-Construction for Nets