MinT - Information on Result #2657784

Information on Result #2657784

Linear OOA(2²⁵⁵, 2741, F₂, 3, 38) (dual of [(2741, 3), 7968, 39]-NRT-code), using 1 step truncation based on linear OOA(2²⁵⁶, 2742, F₂, 3, 39) (dual of [(2742, 3), 7970, 40]-NRT-code), using

OOA 3-folding [i] based on linear OA(2²⁵⁶, 8226, F₂, 39) (dual of [8226, 7970, 40]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2²⁵⁴, 8224, F₂, 39) (dual of [8224, 7970, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(34) [i] based on
    1. linear OA(2²⁴⁸, 8192, F₂, 39) (dual of [8192, 7944, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    2. linear OA(2²²², 8192, F₂, 35) (dual of [8192, 7970, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    3. 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: Constructive and 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		Method
1	Linear OOA(2²⁵⁵, 2255, F₂, 4, 38) (dual of [(2255, 4), 8765, 39]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁵, 2255, F₂, 5, 38) (dual of [(2255, 5), 11020, 39]-NRT-code)	[i]
3	Linear OOA(2²⁵⁵, 2255, F₂, 6, 38) (dual of [(2255, 6), 13275, 39]-NRT-code)	[i]
4	Linear OOA(2²⁵⁵, 2255, F₂, 7, 38) (dual of [(2255, 7), 15530, 39]-NRT-code)	[i]
5	Linear OOA(2²⁵⁵, 2255, F₂, 8, 38) (dual of [(2255, 8), 17785, 39]-NRT-code)	[i]
6	Digital (217, 255, 2255)-net over F₂	[i]