MinT - Information on Result #898707

Information on Result #898707

Linear OOA(16¹²⁸, 65583, F₁₆, 2, 28) (dual of [(65583, 2), 131038, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16¹⁸, 45, F₁₆, 2, 14) (dual of [(45, 2), 72, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,75P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(16¹¹⁰, 65538, F₁₆, 2, 28) (dual of [(65538, 2), 130966, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16¹¹⁰, 131076, F₁₆, 28) (dual of [131076, 130966, 29]-code), using
  - trace code [i] based on linear OA(256⁵⁵, 65538, F₂₅₆, 28) (dual of [65538, 65483, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
      1. linear OA(256⁵⁵, 65536, F₂₅₆, 28) (dual of [65536, 65481, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(256⁵³, 65536, F₂₅₆, 27) (dual of [65536, 65483, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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(16¹²⁸, 9368, F₁₆, 30, 28) (dual of [(9368, 30), 280912, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row