MinT - Information on Result #869075

Information on Result #869075

Linear OOA(32¹⁹, 16385, F₃₂, 2, 7) (dual of [(16385, 2), 32751, 8]-NRT-code), using OOA 2-folding based on linear OA(32¹⁹, 32770, F₃₂, 7) (dual of [32770, 32751, 8]-code), using

discarding factors / shortening the dual code based on linear OA(32¹⁹, 32771, F₃₂, 7) (dual of [32771, 32752, 8]-code), using
- constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
  1. linear OA(32¹⁹, 32768, F₃₂, 7) (dual of [32768, 32749, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  2. linear OA(32¹⁶, 32768, F₃₂, 6) (dual of [32768, 32752, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
  3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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(32²², 16418, F₃₂, 2, 7) (dual of [(16418, 2), 32814, 8]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(32²³, 17410, F₃₂, 2, 7) (dual of [(17410, 2), 34797, 8]-NRT-code)	[i]
3	Linear OOA(32²⁴, 19521, F₃₂, 2, 7) (dual of [(19521, 2), 39018, 8]-NRT-code)	[i]
4	Linear OOA(32⁸⁵, 4210686, F₃₂, 2, 14) (dual of [(4210686, 2), 8421287, 15]-NRT-code)	[i]
5	Linear OOA(32⁹⁰, 4210686, F₃₂, 2, 15) (dual of [(4210686, 2), 8421282, 16]-NRT-code)	[i]
6	OOA(32⁸³, 4210686, S₃₂, 2, 14)	[i]
7	OOA(32⁸⁸, 4210686, S₃₂, 2, 15)	[i]