MinT - Information on Result #1014255

Information on Result #1014255

Linear OOA(8⁴⁸, 174773, F₈, 3, 8) (dual of [(174773, 3), 524271, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁴, 9, F₈, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;23,8) [i]
linear OOA(8⁴⁴, 174764, F₈, 3, 8) (dual of [(174764, 3), 524248, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁴⁴, 524292, F₈, 8) (dual of [524292, 524248, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁴⁴, 524294, F₈, 8) (dual of [524294, 524250, 9]-code), using
    - trace code [i] based on linear OA(64²², 262147, F₆₄, 8) (dual of [262147, 262125, 9]-code), using
      - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        linear OA(64²², 262144, F₆₄, 8) (dual of [262144, 262122, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        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]
        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		This result only	Method
1	Linear OOA(8¹⁷⁰, 5767175, F₈, 3, 16) (dual of [(5767175, 3), 17301355, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs