MinT - Information on Result #1203552

Information on Result #1203552

Digital (29, 43, 299595)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁴³, 299595, F₁₂₈, 14, 14) (dual of [(299595, 14), 4194287, 15]-NRT-code), using

OA 7-folding and stacking [i] based on linear OA(128⁴³, 2097165, F₁₂₈, 14) (dual of [2097165, 2097122, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁴³, 2097167, F₁₂₈, 14) (dual of [2097167, 2097124, 15]-code), using
  - constructionÂ X applied to C_e(13) âŠ‚ C_e(9) [i] based on
    1. linear OA(128⁴⁰, 2097152, F₁₂₈, 14) (dual of [2097152, 2097112, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    2. linear OA(128²⁸, 2097152, F₁₂₈, 10) (dual of [2097152, 2097124, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(128³, 15, F₁₂₈, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), using
      - discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
        Reedâ€“Solomon code RS(125,128) [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 (30, 44, 299595)-net over F₁₂₈	[i]		Net Duplication