MinT - Information on Result #1011985

Information on Result #1011985

Linear OOA(4¹⁰⁴, 5477, F₄, 3, 18) (dual of [(5477, 3), 16327, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹², 14, F₄, 3, 9) (dual of [(14, 3), 30, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,32P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4⁹², 5463, F₄, 3, 18) (dual of [(5463, 3), 16297, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4⁹², 16389, F₄, 18) (dual of [16389, 16297, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁹², 16391, F₄, 18) (dual of [16391, 16299, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
      1. linear OA(4⁹², 16384, F₄, 18) (dual of [16384, 16292, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(4⁸⁵, 16384, F₄, 17) (dual of [16384, 16299, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(4⁰, 7, F₄, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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(4¹⁰⁴, 1825, F₄, 21, 18) (dual of [(1825, 21), 38221, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row