MinT - Information on Result #3179158

Information on Result #3179158

Digital (54, 62, 8196)-net over F₂, using t-expansion based on digital (53, 62, 8196)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁶², 8196, F₂, 9, 9) (dual of [(8196, 9), 73702, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁶², 8196, F₂, 8, 9) (dual of [(8196, 8), 65506, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(2⁶², 32785, F₂, 9) (dual of [32785, 32723, 10]-code), using
    - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
      1. linear OA(2⁶¹, 32768, F₂, 9) (dual of [32768, 32707, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(2⁴⁶, 32768, F₂, 7) (dual of [32768, 32722, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
        strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
      4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (55, 63, 8196)-net over F₂	[i]		Net Duplication