MinT - Information on Result #1682750

Information on Result #1682750

Linear OOA(2¹⁶⁴, 1375, F₂, 7, 26) (dual of [(1375, 7), 9461, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶⁴, 1375, F₂, 3, 26) (dual of [(1375, 3), 3961, 27]-NRT-code), using

1 step truncation [i] based on linear OOA(2¹⁶⁵, 1376, F₂, 3, 27) (dual of [(1376, 3), 3963, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹⁶⁵, 4128, F₂, 27) (dual of [4128, 3963, 28]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2¹⁶³, 4126, F₂, 27) (dual of [4126, 3963, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
      1. linear OA(2¹⁵⁷, 4096, F₂, 27) (dual of [4096, 3939, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2¹³³, 4096, F₂, 23) (dual of [4096, 3963, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-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(2¹⁶⁴, 687, F₂, 35, 26) (dual of [(687, 35), 23881, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row