MinT - Information on Result #3179397

Information on Result #3179397

Digital (63, 73, 3280)-net over F₂, using t-expansion based on digital (62, 73, 3280)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁷³, 3280, F₂, 11, 11) (dual of [(3280, 11), 36007, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2⁷³, 16401, F₂, 11) (dual of [16401, 16328, 12]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(2⁷², 16400, F₂, 11) (dual of [16400, 16328, 12]-code), using
    - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
      1. linear OA(2⁷¹, 16384, F₂, 11) (dual of [16384, 16313, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(2⁵⁷, 16384, F₂, 9) (dual of [16384, 16327, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(2¹⁵, 16, F₂, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
        dual of repetition code with length 16 [i]
      4. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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 (64, 74, 3280)-net over F₂	[i]		Net Duplication