MinT - Information on Result #1051307

Information on Result #1051307

Linear OOA(2⁸⁷, 32772, F₂, 4, 11) (dual of [(32772, 4), 131001, 12]-NRT-code), using OOA 4-folding based on linear OA(2⁸⁷, 131088, F₂, 11) (dual of [131088, 131001, 12]-code), using

discarding factors / shortening the dual code based on linear OA(2⁸⁷, 131090, F₂, 11) (dual of [131090, 131003, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(8) [i] based on
  1. linear OA(2⁸⁶, 131072, F₂, 11) (dual of [131072, 130986, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(2⁶⁹, 131072, F₂, 9) (dual of [131072, 131003, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  3. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 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(2⁸⁷, 32772, F₂, 4, 10) (dual of [(32772, 4), 131001, 11]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2⁸⁷, 32772, F₂, 5, 11) (dual of [(32772, 5), 163773, 12]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2⁸⁷, 32772, F₂, 6, 11) (dual of [(32772, 6), 196545, 12]-NRT-code)	[i]
4	Linear OOA(2⁸⁷, 32772, F₂, 7, 11) (dual of [(32772, 7), 229317, 12]-NRT-code)	[i]
5	Linear OOA(2⁸⁷, 32772, F₂, 8, 11) (dual of [(32772, 8), 262089, 12]-NRT-code)	[i]
6	Digital (76, 87, 32772)-net over F₂	[i]