MinT - Information on Result #2480315

Information on Result #2480315

Linear OOA(2²³⁷, 2064, F₂, 2, 38) (dual of [(2064, 2), 3891, 39]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²³⁵, 2063, F₂, 2, 38) (dual of [(2063, 2), 3891, 39]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²³⁵, 4126, F₂, 38) (dual of [4126, 3891, 39]-code), using
- strength reduction [i] based on linear OA(2²³⁵, 4126, F₂, 39) (dual of [4126, 3891, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(34) [i] based on
    1. linear OA(2²²⁹, 4096, F₂, 39) (dual of [4096, 3867, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    2. linear OA(2²⁰⁵, 4096, F₂, 35) (dual of [4096, 3891, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [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: 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(2²³⁸, 2064, F₂, 2, 38) (dual of [(2064, 2), 3890, 39]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³⁷, 1410, F₂, 3, 38) (dual of [(1410, 3), 3993, 39]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²³⁷, 1410, F₂, 4, 38) (dual of [(1410, 4), 5403, 39]-NRT-code)	[i]
4	Linear OOA(2²³⁷, 1410, F₂, 5, 38) (dual of [(1410, 5), 6813, 39]-NRT-code)	[i]
5	Linear OOA(2²³⁷, 1410, F₂, 6, 38) (dual of [(1410, 6), 8223, 39]-NRT-code)	[i]
6	Linear OOA(2²³⁷, 1410, F₂, 7, 38) (dual of [(1410, 7), 9633, 39]-NRT-code)	[i]
7	Linear OOA(2²³⁷, 1410, F₂, 8, 38) (dual of [(1410, 8), 11043, 39]-NRT-code)	[i]
8	Digital (199, 237, 1410)-net over F₂	[i]