MinT - Information on Result #1013359

Information on Result #1013359

Linear OOA(5⁹⁸, 5228, F₅, 3, 18) (dual of [(5228, 3), 15586, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹³, 18, F₅, 3, 9) (dual of [(18, 3), 41, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,44P) [i] based on function field F/F₅ with g(F) = 4 and N(F) ≥ 18, using
  - an explicitly constructive algebraic function field [i]
linear OOA(5⁸⁵, 5210, F₅, 3, 18) (dual of [(5210, 3), 15545, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁸⁵, 15630, F₅, 18) (dual of [15630, 15545, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁸⁵, 15631, F₅, 18) (dual of [15631, 15546, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
      1. linear OA(5⁸⁵, 15625, F₅, 18) (dual of [15625, 15540, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(5⁷⁹, 15625, F₅, 17) (dual of [15625, 15546, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(5⁰, 6, F₅, 0) (dual of [6, 6, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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(5⁹⁸, 1742, F₅, 21, 18) (dual of [(1742, 21), 36484, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row