MinT - Information on Result #1195454

Information on Result #1195454

Digital (64, 84, 13109)-net over F₁₆, using net defined by OOA based on linear OOA(16⁸⁴, 13109, F₁₆, 20, 20) (dual of [(13109, 20), 262096, 21]-NRT-code), using

OA 10-folding and stacking [i] based on linear OA(16⁸⁴, 131090, F₁₆, 20) (dual of [131090, 131006, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁸⁴, 131094, F₁₆, 20) (dual of [131094, 131010, 21]-code), using
  - trace code [i] based on linear OA(256⁴², 65547, F₂₅₆, 20) (dual of [65547, 65505, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(15) [i] based on
      1. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(256³¹, 65536, F₂₅₆, 16) (dual of [65536, 65505, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
        discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
        Reedâ€“Solomon code RS(253,256) [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 (65, 85, 13109)-net over F₁₆	[i]		Net Duplication