MinT - Information on Result #1051598

Information on Result #1051598

Linear OOA(2¹¹³, 16388, F₂, 4, 14) (dual of [(16388, 4), 65439, 15]-NRT-code), using OOA 4-folding based on linear OA(2¹¹³, 65552, F₂, 14) (dual of [65552, 65439, 15]-code), using

discarding factors / shortening the dual code based on linear OA(2¹¹³, 65553, F₂, 14) (dual of [65553, 65440, 15]-code), using
- 1 times truncation [i] based on linear OA(2¹¹⁴, 65554, F₂, 15) (dual of [65554, 65440, 16]-code), using
  - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
    1. 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]
    2. linear OA(2⁹⁷, 65536, F₂, 13) (dual of [65536, 65439, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(2¹¹³, 16388, F₂, 5, 14) (dual of [(16388, 5), 81827, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹¹³, 16388, F₂, 6, 14) (dual of [(16388, 6), 98215, 15]-NRT-code)	[i]
3	Linear OOA(2¹¹³, 16388, F₂, 7, 14) (dual of [(16388, 7), 114603, 15]-NRT-code)	[i]
4	Linear OOA(2¹¹³, 16388, F₂, 8, 14) (dual of [(16388, 8), 130991, 15]-NRT-code)	[i]
5	Digital (99, 113, 16388)-net over F₂	[i]