MinT - Information on Result #2611117

Information on Result #2611117

Linear OOA(2⁹⁷, 174769, F₂, 3, 10) (dual of [(174769, 3), 524210, 11]-NRT-code), using strength reduction based on linear OOA(2⁹⁷, 174769, F₂, 3, 11) (dual of [(174769, 3), 524210, 12]-NRT-code), using

OOA 3-folding [i] based on linear OA(2⁹⁷, 524307, F₂, 11) (dual of [524307, 524210, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁹⁷, 524308, F₂, 11) (dual of [524308, 524211, 12]-code), using
  - constructionÂ X applied to C_e(10) âŠ‚ C_e(8) [i] based on
    1. linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(2⁷⁷, 524288, F₂, 9) (dual of [524288, 524211, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    3. linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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(2⁹⁷, 155717, F₂, 4, 10) (dual of [(155717, 4), 622771, 11]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁹⁷, 155717, F₂, 5, 10) (dual of [(155717, 5), 778488, 11]-NRT-code)	[i]
3	Linear OOA(2⁹⁷, 155717, F₂, 6, 10) (dual of [(155717, 6), 934205, 11]-NRT-code)	[i]
4	Linear OOA(2⁹⁷, 155717, F₂, 7, 10) (dual of [(155717, 7), 1089922, 11]-NRT-code)	[i]
5	Linear OOA(2⁹⁷, 155717, F₂, 8, 10) (dual of [(155717, 8), 1245639, 11]-NRT-code)	[i]
6	Digital (87, 97, 155717)-net over F₂	[i]