MinT - Information on Result #1679910

Information on Result #1679910

Linear OOA(2¹⁰², 4023, F₂, 7, 15) (dual of [(4023, 7), 28059, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰², 4023, F₂, 4, 15) (dual of [(4023, 4), 15990, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁰², 4100, F₂, 4, 15) (dual of [(4100, 4), 16298, 16]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2¹⁰⁰, 4100, F₂, 4, 15) (dual of [(4100, 4), 16300, 16]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁰⁰, 16400, F₂, 15) (dual of [16400, 16300, 16]-code), using
    - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
      1. linear OA(2⁹⁹, 16384, F₂, 15) (dual of [16384, 16285, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(2⁸⁵, 16384, F₂, 13) (dual of [16384, 16299, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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: 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(2¹⁰², 4022, F₂, 8, 15) (dual of [(4022, 8), 32074, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁰², 4022, F₂, 21, 15) (dual of [(4022, 21), 84360, 16]-NRT-code)	[i]		OOA Stacking with Additional Row