MinT - Information on Result #1016520

Information on Result #1016520

Linear OOA(9¹⁴⁹, 19712, F₉, 3, 30) (dual of [(19712, 3), 58987, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹⁸, 28, F₉, 3, 15) (dual of [(28, 3), 66, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,68P) [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(9¹³¹, 19684, F₉, 3, 30) (dual of [(19684, 3), 58921, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9¹³¹, 59052, F₉, 30) (dual of [59052, 58921, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹³¹, 59054, F₉, 30) (dual of [59054, 58923, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
      1. linear OA(9¹³¹, 59049, F₉, 30) (dual of [59049, 58918, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(9¹²⁶, 59049, F₉, 29) (dual of [59049, 58923, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(9¹⁴⁹, 3942, F₉, 33, 30) (dual of [(3942, 33), 129937, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row