MinT - Information on Result #1016126

Information on Result #1016126

Linear OOA(9⁶⁵, 19712, F₉, 3, 13) (dual of [(19712, 3), 59071, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9⁹, 28, F₉, 3, 6) (dual of [(28, 3), 75, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,77P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OOA(9⁵⁶, 19684, F₉, 3, 13) (dual of [(19684, 3), 58996, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9⁵⁶, 59052, F₉, 13) (dual of [59052, 58996, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁵⁶, 59054, F₉, 13) (dual of [59054, 58998, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(9⁵⁶, 59049, F₉, 13) (dual of [59049, 58993, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(9⁵¹, 59049, F₉, 12) (dual of [59049, 58998, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(9⁰, 5, F₉, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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(9⁶⁵, 9855, F₉, 15, 13) (dual of [(9855, 15), 147760, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row