MinT - Information on Result #1679235

Information on Result #1679235

Linear OOA(2⁷⁸, 686, F₂, 7, 14) (dual of [(686, 7), 4724, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁷⁸, 686, F₂, 3, 14) (dual of [(686, 3), 1980, 15]-NRT-code), using

OOA 3-folding [i] based on linear OA(2⁷⁸, 2058, F₂, 14) (dual of [2058, 1980, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁷⁸, 2059, F₂, 14) (dual of [2059, 1981, 15]-code), using
  - 1 times truncation [i] based on linear OA(2⁷⁹, 2060, F₂, 15) (dual of [2060, 1981, 16]-code), using
    - constructionÂ X applied to C_e(14) âŠ‚ C_e(12) [i] based on
      1. linear OA(2⁷⁸, 2048, F₂, 15) (dual of [2048, 1970, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(2⁶⁷, 2048, F₂, 13) (dual of [2048, 1981, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 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(2⁷⁹, 686, F₂, 7, 14) (dual of [(686, 7), 4723, 15]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2⁷⁸, 685, F₂, 8, 14) (dual of [(685, 8), 5402, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
3	Linear OOA(2⁷⁸, 685, F₂, 21, 14) (dual of [(685, 21), 14307, 15]-NRT-code)	[i]		OOA Stacking with Additional Row