MinT - Information on Result #1598786

Information on Result #1598786

Linear OOA(2²³⁹, 901, F₂, 4, 43) (dual of [(901, 4), 3365, 44]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁹, 901, F₂, 2, 43) (dual of [(901, 2), 1563, 44]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁹, 1038, F₂, 2, 43) (dual of [(1038, 2), 1837, 44]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²³⁸, 1038, F₂, 2, 43) (dual of [(1038, 2), 1838, 44]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²³⁸, 2076, F₂, 43) (dual of [2076, 1838, 44]-code), using
    - constructionÂ X applied to C_e(42) âŠ‚ C_e(38) [i] based on
      1. 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]
      2. 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]
      3. linear OA(2⁶, 28, F₂, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [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(2²³⁹, 450, F₂, 7, 43) (dual of [(450, 7), 2911, 44]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²³⁹, 450, F₂, 8, 43) (dual of [(450, 8), 3361, 44]-NRT-code)	[i]		OOA Folding