MinT - Information on Result #903586

Information on Result #903586

Linear OOA(64³⁰, 131153, F₆₄, 2, 9) (dual of [(131153, 2), 262276, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64⁵, 80, F₆₄, 2, 4) (dual of [(80, 2), 155, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,155P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
  - a function field by SÃ©mirat [i]
linear OOA(64²⁵, 131073, F₆₄, 2, 9) (dual of [(131073, 2), 262121, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64²⁵, 262146, F₆₄, 9) (dual of [262146, 262121, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(64²⁵, 262147, F₆₄, 9) (dual of [262147, 262122, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(64²⁵, 262144, F₆₄, 9) (dual of [262144, 262119, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. 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]
      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		This result only	Method
1	Linear OOA(64³⁰, 65576, F₆₄, 10, 9) (dual of [(65576, 10), 655730, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row