MinT - Information on Result #1051831

Information on Result #1051831

Linear OOA(2¹³², 16389, F₂, 4, 16) (dual of [(16389, 4), 65424, 17]-NRT-code), using OOA 4-folding based on linear OA(2¹³², 65556, F₂, 16) (dual of [65556, 65424, 17]-code), using

3 times code embedding in larger space [i] based on linear OA(2¹²⁹, 65553, F₂, 16) (dual of [65553, 65424, 17]-code), using
- 1 times truncation [i] based on linear OA(2¹³⁰, 65554, F₂, 17) (dual of [65554, 65424, 18]-code), using
  - constructionÂ X4 applied to C_e(16) âŠ‚ C_e(14) [i] based on
    1. linear OA(2¹²⁹, 65536, F₂, 17) (dual of [65536, 65407, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(2¹¹³, 65536, F₂, 15) (dual of [65536, 65423, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    3. linear OA(2¹⁷, 18, F₂, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
      - dual of repetition code with length 18 [i]
    4. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹³³, 16389, F₂, 4, 16) (dual of [(16389, 4), 65423, 17]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹³², 15613, F₂, 5, 16) (dual of [(15613, 5), 77933, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹³², 15613, F₂, 6, 16) (dual of [(15613, 6), 93546, 17]-NRT-code)	[i]
4	Linear OOA(2¹³², 15613, F₂, 7, 16) (dual of [(15613, 7), 109159, 17]-NRT-code)	[i]
5	Linear OOA(2¹³², 15613, F₂, 8, 16) (dual of [(15613, 8), 124772, 17]-NRT-code)	[i]
6	Digital (116, 132, 15613)-net over F₂	[i]