MinT - Information on Result #1096770

Information on Result #1096770

Linear OOA(2²¹³, 6557, F₂, 5, 28) (dual of [(6557, 5), 32572, 29]-NRT-code), using OOA 5-folding based on linear OA(2²¹³, 32785, F₂, 28) (dual of [32785, 32572, 29]-code), using

2 times code embedding in larger space [i] based on linear OA(2²¹¹, 32783, F₂, 28) (dual of [32783, 32572, 29]-code), using
- 1 times truncation [i] based on linear OA(2²¹², 32784, F₂, 29) (dual of [32784, 32572, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
    1. linear OA(2²¹¹, 32768, F₂, 29) (dual of [32768, 32557, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    3. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2²¹⁴, 6557, F₂, 5, 28) (dual of [(6557, 5), 32571, 29]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²¹⁵, 6557, F₂, 5, 28) (dual of [(6557, 5), 32570, 29]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²¹³, 6321, F₂, 6, 28) (dual of [(6321, 6), 37713, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2²¹³, 6321, F₂, 7, 28) (dual of [(6321, 7), 44034, 29]-NRT-code)	[i]
5	Linear OOA(2²¹³, 6321, F₂, 8, 28) (dual of [(6321, 8), 50355, 29]-NRT-code)	[i]
6	Digital (185, 213, 6321)-net over F₂	[i]