MinT - Information on Result #1518818

Information on Result #1518818

Linear OOA(2²⁴⁵, 851, F₂, 3, 45) (dual of [(851, 3), 2308, 46]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁵, 851, F₂, 2, 45) (dual of [(851, 2), 1457, 46]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁵, 1030, F₂, 2, 45) (dual of [(1030, 2), 1815, 46]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²⁴⁴, 1030, F₂, 2, 45) (dual of [(1030, 2), 1816, 46]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²⁴⁴, 2060, F₂, 45) (dual of [2060, 1816, 46]-code), using
    - constructionÂ X applied to C_e(44) âŠ‚ C_e(42) [i] based on
      1. linear OA(2²⁴³, 2048, F₂, 45) (dual of [2048, 1805, 46]-code), using an extension C_e(44) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,44], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 45 [i]
      2. linear OA(2²³², 2048, F₂, 43) (dual of [2048, 1816, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [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(2²⁴⁵, 425, F₂, 5, 45) (dual of [(425, 5), 1880, 46]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴⁵, 425, F₂, 6, 45) (dual of [(425, 6), 2305, 46]-NRT-code)	[i]		OOA Folding