MinT - Information on Result #1053438

Information on Result #1053438

Linear OOA(2¹⁹², 2057, F₂, 4, 29) (dual of [(2057, 4), 8036, 30]-NRT-code), using OOA 4-folding based on linear OA(2¹⁹², 8228, F₂, 29) (dual of [8228, 8036, 30]-code), using

3 times code embedding in larger space [i] based on linear OA(2¹⁸⁹, 8225, F₂, 29) (dual of [8225, 8036, 30]-code), using
- constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(2¹⁸³, 8193, F₂, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(2¹⁵⁷, 8193, F₂, 25) (dual of [8193, 8036, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [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(2¹⁹², 2057, F₂, 4, 28) (dual of [(2057, 4), 8036, 29]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁹³, 2057, F₂, 4, 29) (dual of [(2057, 4), 8035, 30]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁴, 2057, F₂, 4, 29) (dual of [(2057, 4), 8034, 30]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2¹⁹¹, 2056, F₂, 4, 28) (dual of [(2056, 4), 8033, 29]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(2¹⁹², 2057, F₂, 5, 29) (dual of [(2057, 5), 10093, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
6	Linear OOA(2¹⁹², 2057, F₂, 6, 29) (dual of [(2057, 6), 12150, 30]-NRT-code)	[i]
7	Linear OOA(2¹⁹², 2057, F₂, 7, 29) (dual of [(2057, 7), 14207, 30]-NRT-code)	[i]
8	Linear OOA(2¹⁹², 2057, F₂, 8, 29) (dual of [(2057, 8), 16264, 30]-NRT-code)	[i]
9	Digital (163, 192, 2057)-net over F₂	[i]