MinT - Information on Result #1198752

Information on Result #1198752

Digital (14, 19, 524322)-net over F₃₂, using net defined by OOA based on linear OOA(32¹⁹, 524322, F₃₂, 6, 5) (dual of [(524322, 6), 3145913, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(32¹⁹, 524323, F₃₂, 2, 5) (dual of [(524323, 2), 1048627, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;64,32) [i]
  2. linear OOA(32¹⁷, 524290, F₃₂, 2, 5) (dual of [(524290, 2), 1048563, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(32¹⁷, 1048580, F₃₂, 5) (dual of [1048580, 1048563, 6]-code), using
      - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(32¹⁷, 1048576, F₃₂, 5) (dual of [1048576, 1048559, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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 (55, 65, 2202042)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets
2	Digital (59, 70, 2202042)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets