MinT - Information on Result #1194240

Information on Result #1194240

Digital (64, 84, 1314)-net over F₉, using net defined by OOA based on linear OOA(9⁸⁴, 1314, F₉, 20, 20) (dual of [(1314, 20), 26196, 21]-NRT-code), using

OA 10-folding and stacking [i] based on linear OA(9⁸⁴, 13140, F₉, 20) (dual of [13140, 13056, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁸⁴, 13144, F₉, 20) (dual of [13144, 13060, 21]-code), using
  - trace code [i] based on linear OA(81⁴², 6572, F₈₁, 20) (dual of [6572, 6530, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(15) [i] based on
      1. linear OA(81³⁹, 6561, F₈₁, 20) (dual of [6561, 6522, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(81³¹, 6561, F₈₁, 16) (dual of [6561, 6530, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(81³, 11, F₈₁, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
        discarding factors / shortening the dual code based on linear OA(81³, 81, F₈₁, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
        Reedâ€“Solomon code RS(78,81) [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, 1314)-net over F₉	[i]		Net Duplication