MinT - Information on Result #2844936

Information on Result #2844936

Linear OOA(2²¹², 6556, F₂, 5, 28) (dual of [(6556, 5), 32568, 29]-NRT-code), using strength reduction based on linear OOA(2²¹², 6556, F₂, 5, 29) (dual of [(6556, 5), 32568, 30]-NRT-code), using

OOA 5-folding [i] based on linear OA(2²¹², 32780, F₂, 29) (dual of [32780, 32568, 30]-code), using
- discarding factors / shortening the dual code 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(2²¹², 6124, F₂, 6, 28) (dual of [(6124, 6), 36532, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹², 6124, F₂, 7, 28) (dual of [(6124, 7), 42656, 29]-NRT-code)	[i]
3	Linear OOA(2²¹², 6124, F₂, 8, 28) (dual of [(6124, 8), 48780, 29]-NRT-code)	[i]
4	Digital (184, 212, 6124)-net over F₂	[i]