MinT - Information on Result #979380

Information on Result #979380

Linear OOA(8⁷⁶, 10924, F₈, 3, 18) (dual of [(10924, 3), 32696, 19]-NRT-code), using OOA 3-folding based on linear OA(8⁷⁶, 32772, F₈, 18) (dual of [32772, 32696, 19]-code), using

discarding factors / shortening the dual code based on linear OA(8⁷⁶, 32773, F₈, 18) (dual of [32773, 32697, 19]-code), using
- constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
  1. linear OA(8⁷⁶, 32768, F₈, 18) (dual of [32768, 32692, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
  2. linear OA(8⁷¹, 32768, F₈, 17) (dual of [32768, 32697, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [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(8⁷⁷, 10924, F₈, 3, 18) (dual of [(10924, 3), 32695, 19]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(8⁸⁶, 10938, F₈, 3, 18) (dual of [(10938, 3), 32728, 19]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(8⁸⁷, 10941, F₈, 3, 18) (dual of [(10941, 3), 32736, 19]-NRT-code)	[i]
4	Linear OOA(8⁸⁸, 10948, F₈, 3, 18) (dual of [(10948, 3), 32756, 19]-NRT-code)	[i]
5	Linear OOA(8⁸⁹, 10949, F₈, 3, 18) (dual of [(10949, 3), 32758, 19]-NRT-code)	[i]
6	Linear OOA(8⁹⁰, 10952, F₈, 3, 18) (dual of [(10952, 3), 32766, 19]-NRT-code)	[i]