MinT - Information on Result #898466

Information on Result #898466

Linear OOA(16⁸⁹, 65562, F₁₆, 2, 20) (dual of [(65562, 2), 131035, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16¹¹, 24, F₁₆, 2, 10) (dual of [(24, 2), 37, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,37P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
  - a function field by SÃ©mirat [i]
linear OOA(16⁷⁸, 65538, F₁₆, 2, 20) (dual of [(65538, 2), 130998, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁷⁸, 131076, F₁₆, 20) (dual of [131076, 130998, 21]-code), using
  - trace code [i] based on linear OA(256³⁹, 65538, F₂₅₆, 20) (dual of [65538, 65499, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(256³⁷, 65536, F₂₅₆, 19) (dual of [65536, 65499, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 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(16⁸⁹, 13112, F₁₆, 22, 20) (dual of [(13112, 22), 288375, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row