MinT - Information on Result #1195724

Information on Result #1195724

Digital (94, 122, 9365)-net over F₁₆, using net defined by OOA based on linear OOA(16¹²², 9365, F₁₆, 28, 28) (dual of [(9365, 28), 262098, 29]-NRT-code), using

OA 14-folding and stacking [i] based on linear OA(16¹²², 131110, F₁₆, 28) (dual of [131110, 130988, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹²², 131112, F₁₆, 28) (dual of [131112, 130990, 29]-code), using
  - trace code [i] based on linear OA(256⁶¹, 65556, F₂₅₆, 28) (dual of [65556, 65495, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(20) [i] based on
      1. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(256⁴¹, 65536, F₂₅₆, 21) (dual of [65536, 65495, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(256⁶, 20, F₂₅₆, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁶, 256, F₂₅₆, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
        Reedâ€“Solomon code RS(250,256) [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 (95, 123, 9365)-net over F₁₆	[i]		Net Duplication