MinT - Information on Result #1680920

Information on Result #1680920

Linear OOA(2¹²⁸, 58235, F₂, 7, 14) (dual of [(58235, 7), 407517, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²⁸, 58235, F₂, 4, 14) (dual of [(58235, 4), 232812, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹²⁸, 65541, F₂, 4, 14) (dual of [(65541, 4), 262036, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹²⁸, 262164, F₂, 14) (dual of [262164, 262036, 15]-code), using
  - strength reduction [i] based on linear OA(2¹²⁸, 262164, F₂, 15) (dual of [262164, 262036, 16]-code), using
    - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
      1. linear OA(2¹²⁷, 262144, F₂, 15) (dual of [262144, 262017, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(2¹⁰⁹, 262144, F₂, 13) (dual of [262144, 262035, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(2¹⁹, 20, F₂, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
        dual of repetition code with length 20 [i]
      4. linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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(2¹²⁸, 58234, F₂, 8, 14) (dual of [(58234, 8), 465744, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹²⁸, 58234, F₂, 21, 14) (dual of [(58234, 21), 1222786, 15]-NRT-code)	[i]		OOA Stacking with Additional Row