MinT - Information on Result #898292

Information on Result #898292

Linear OOA(16⁵⁵, 65576, F₁₆, 2, 12) (dual of [(65576, 2), 131097, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16⁹, 38, F₁₆, 2, 6) (dual of [(38, 2), 67, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,69P) [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
  - a function field by SÃ©mirat [i]
linear OOA(16⁴⁶, 65538, F₁₆, 2, 12) (dual of [(65538, 2), 131030, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁴⁶, 131076, F₁₆, 12) (dual of [131076, 131030, 13]-code), using
  - trace code [i] based on linear OA(256²³, 65538, F₂₅₆, 12) (dual of [65538, 65515, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(256²³, 65536, F₂₅₆, 12) (dual of [65536, 65513, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(256²¹, 65536, F₂₅₆, 11) (dual of [65536, 65515, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(16⁵⁵, 21858, F₁₆, 14, 12) (dual of [(21858, 14), 305957, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row