MinT - Information on Result #1195190

Information on Result #1195190

Digital (45, 59, 18727)-net over F₁₆, using net defined by OOA based on linear OOA(16⁵⁹, 18727, F₁₆, 14, 14) (dual of [(18727, 14), 262119, 15]-NRT-code), using

OA 7-folding and stacking [i] based on linear OA(16⁵⁹, 131089, F₁₆, 14) (dual of [131089, 131030, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16⁵⁸, 131088, F₁₆, 14) (dual of [131088, 131030, 15]-code), using
  - trace code [i] based on linear OA(256²⁹, 65544, F₂₅₆, 14) (dual of [65544, 65515, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(10) [i] based on
      1. linear OA(256²⁷, 65536, F₂₅₆, 14) (dual of [65536, 65509, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(256²¹, 65536, F₂₅₆, 11) (dual of [65536, 65515, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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		This result only	Method
1	Digital (46, 60, 18727)-net over F₁₆	[i]		Net Duplication