MinT - Information on Result #898253

Information on Result #898253

Linear OOA(16³⁰, 2073, F₁₆, 2, 9) (dual of [(2073, 2), 4116, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16⁵, 24, F₁₆, 2, 4) (dual of [(24, 2), 43, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,43P) [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(16²⁵, 2049, F₁₆, 2, 9) (dual of [(2049, 2), 4073, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16²⁵, 4098, F₁₆, 9) (dual of [4098, 4073, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²⁵, 4099, F₁₆, 9) (dual of [4099, 4074, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(16²⁵, 4096, F₁₆, 9) (dual of [4096, 4071, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(16²², 4096, F₁₆, 8) (dual of [4096, 4074, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(16⁰, 3, F₁₆, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(16³⁰, 1036, F₁₆, 10, 9) (dual of [(1036, 10), 10330, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row