MinT - Information on Result #1688181

Information on Result #1688181

Linear OOA(2²⁴⁰, 40396, F₂, 7, 26) (dual of [(40396, 7), 282532, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁰, 40396, F₂, 6, 26) (dual of [(40396, 6), 242136, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁰, 43695, F₂, 6, 26) (dual of [(43695, 6), 261930, 27]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2²⁴⁰, 262170, F₂, 26) (dual of [262170, 261930, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁴⁰, 262175, F₂, 26) (dual of [262175, 261935, 27]-code), using
    - 1 times truncation [i] based on linear OA(2²⁴¹, 262176, F₂, 27) (dual of [262176, 261935, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
        linear OA(2²³⁵, 262144, F₂, 27) (dual of [262144, 261909, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(2¹⁹⁹, 262144, F₂, 23) (dual of [262144, 261945, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        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(2²⁴⁰, 20197, F₂, 35, 26) (dual of [(20197, 35), 706655, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row