MinT - Information on Result #984282

Information on Result #984282

Linear OOA(9³⁴, 354299, F₉, 3, 6) (dual of [(354299, 3), 1062863, 7]-NRT-code), using OOA 3-folding based on linear OA(9³⁴, 1062897, F₉, 6) (dual of [1062897, 1062863, 7]-code), using

discarding factors / shortening the dual code based on linear OA(9³⁴, 1062898, F₉, 6) (dual of [1062898, 1062864, 7]-code), using
- trace code [i] based on linear OA(81¹⁷, 531449, F₈₁, 6) (dual of [531449, 531432, 7]-code), using
  - constructionÂ X4 applied to C_e(5) âŠ‚ C_e(3) [i] based on
    1. linear OA(81¹⁶, 531441, F₈₁, 6) (dual of [531441, 531425, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    2. linear OA(81¹⁰, 531441, F₈₁, 4) (dual of [531441, 531431, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(81⁷, 8, F₈₁, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,81)), using
      - dual of repetition code with length 8 [i]
    4. linear OA(81¹, 8, F₈₁, 1) (dual of [8, 7, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(81¹, 81, F₈₁, 1) (dual of [81, 80, 2]-code), using
        Reedâ€“Solomon code RS(80,81) [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		This result only	Method
1	Linear OOA(9¹²⁴, 5946701, F₉, 3, 12) (dual of [(5946701, 3), 17839979, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(9¹³², 5946701, F₉, 3, 13) (dual of [(5946701, 3), 17839971, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs