MinT - Information on Result #1117168

Information on Result #1117168

Linear OOA(3⁷⁰, 3945, F₃, 5, 11) (dual of [(3945, 5), 19655, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶, 7, F₃, 5, 5) (dual of [(7, 5), 29, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3⁶, 7, F₃, 4, 5) (dual of [(7, 4), 22, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,22P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3⁶⁴, 3938, F₃, 5, 11) (dual of [(3938, 5), 19626, 12]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3⁶⁴, 19690, F₃, 11) (dual of [19690, 19626, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶⁴, 19692, F₃, 11) (dual of [19692, 19628, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
      1. linear OA(3⁶⁴, 19683, F₃, 11) (dual of [19683, 19619, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(3⁵⁵, 19683, F₃, 10) (dual of [19683, 19628, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(3⁰, 9, F₃, 0) (dual of [9, 9, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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(3⁷⁰, 3944, F₃, 15, 11) (dual of [(3944, 15), 59090, 12]-NRT-code)	[i]		OOA Stacking with Additional Row