MinT - Information on Result #1631336

Information on Result #1631336

Linear OOA(2¹¹³, 16388, F₂, 5, 14) (dual of [(16388, 5), 81827, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹³, 16388, F₂, 4, 14) (dual of [(16388, 4), 65439, 15]-NRT-code), using

OOA 4-folding [i] 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: 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		This result only	Method
1	Linear OOA(2¹¹⁴, 16388, F₂, 5, 14) (dual of [(16388, 5), 81826, 15]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹¹⁵, 16388, F₂, 5, 14) (dual of [(16388, 5), 81825, 15]-NRT-code)	[i]		OOA Duplication