MinT - Information on Result #1597263

Information on Result #1597263

Linear OOA(2²²³, 868, F₂, 4, 40) (dual of [(868, 4), 3249, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²³, 868, F₂, 2, 40) (dual of [(868, 2), 1513, 41]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²³, 1030, F₂, 2, 40) (dual of [(1030, 2), 1837, 41]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²²², 1030, F₂, 2, 40) (dual of [(1030, 2), 1838, 41]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²²², 2060, F₂, 40) (dual of [2060, 1838, 41]-code), using
    - strength reduction [i] based on linear OA(2²²², 2060, F₂, 41) (dual of [2060, 1838, 42]-code), using
      - constructionÂ X applied to C_e(40) âŠ‚ C_e(38) [i] based on
        linear OA(2²²¹, 2048, F₂, 41) (dual of [2048, 1827, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
        linear OA(2²¹⁰, 2048, F₂, 39) (dual of [2048, 1838, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
        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(2²²³, 434, F₂, 7, 40) (dual of [(434, 7), 2815, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²²³, 434, F₂, 8, 40) (dual of [(434, 8), 3249, 41]-NRT-code)	[i]		OOA Folding