MinT - Information on Result #978812

Information on Result #978812

Linear OOA(8⁴⁰, 174768, F₈, 3, 7) (dual of [(174768, 3), 524264, 8]-NRT-code), using OOA 3-folding based on linear OA(8⁴⁰, 524304, F₈, 7) (dual of [524304, 524264, 8]-code), using

discarding factors / shortening the dual code based on linear OA(8⁴⁰, 524306, F₈, 7) (dual of [524306, 524266, 8]-code), using
- trace code [i] based on linear OA(64²⁰, 262153, F₆₄, 7) (dual of [262153, 262133, 8]-code), using
  - constructionÂ X4 applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
    1. linear OA(64¹⁹, 262145, F₆₄, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
    2. linear OA(64¹³, 262145, F₆₄, 5) (dual of [262145, 262132, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
    3. linear OA(64⁷, 8, F₆₄, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
      - dual of repetition code with length 8 [i]
    4. linear OA(64¹, 8, F₆₄, 1) (dual of [8, 7, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹, 64, F₆₄, 1) (dual of [64, 63, 2]-code), using
        Reedâ€“Solomon code RS(63,64) [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(8¹⁴⁶, 5767170, F₈, 3, 14) (dual of [(5767170, 3), 17301364, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹⁵⁴, 5767170, F₈, 3, 15) (dual of [(5767170, 3), 17301356, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs