MinT - Information on Result #1195648

Information on Result #1195648

Digital (78, 103, 10924)-net over F₁₆, using net defined by OOA based on linear OOA(16¹⁰³, 10924, F₁₆, 25, 25) (dual of [(10924, 25), 272997, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(16¹⁰³, 131089, F₁₆, 25) (dual of [131089, 130986, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16¹⁰², 131088, F₁₆, 25) (dual of [131088, 130986, 26]-code), using
  - trace code [i] based on linear OA(256⁵¹, 65544, F₂₅₆, 25) (dual of [65544, 65493, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
      1. linear OA(256⁴⁹, 65536, F₂₅₆, 25) (dual of [65536, 65487, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(256⁴³, 65536, F₂₅₆, 22) (dual of [65536, 65493, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
        discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
        Reedâ€“Solomon code RS(254,256) [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		Method
1	Digital (79, 104, 10924)-net over F₁₆	[i]	Net Duplication
2	Digital (80, 105, 10924)-net over F₁₆	[i]
3	Digital (81, 106, 10924)-net over F₁₆	[i]