MinT - Information on Result #978810

Information on Result #978810

Linear OOA(8³⁸, 174764, F₈, 3, 7) (dual of [(174764, 3), 524254, 8]-NRT-code), using OOA 3-folding based on linear OA(8³⁸, 524292, F₈, 7) (dual of [524292, 524254, 8]-code), using

discarding factors / shortening the dual code based on linear OA(8³⁸, 524294, F₈, 7) (dual of [524294, 524256, 8]-code), using
- trace code [i] based on linear OA(64¹⁹, 262147, F₆₄, 7) (dual of [262147, 262128, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(64¹⁹, 262144, F₆₄, 7) (dual of [262144, 262125, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(64¹⁶, 262144, F₆₄, 6) (dual of [262144, 262128, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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(8⁴¹, 174773, F₈, 3, 7) (dual of [(174773, 3), 524278, 8]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(8⁴², 174829, F₈, 3, 7) (dual of [(174829, 3), 524445, 8]-NRT-code)	[i]
3	Linear OOA(8¹⁴⁴, 5767166, F₈, 3, 14) (dual of [(5767166, 3), 17301354, 15]-NRT-code)	[i]
4	Linear OOA(8¹⁵², 5767166, F₈, 3, 15) (dual of [(5767166, 3), 17301346, 16]-NRT-code)	[i]