MinT - Information on Result #1297181

Information on Result #1297181

Linear OA(256³⁷, 65827, F₂₅₆, 15) (dual of [65827, 65790, 16]-code), using (u,Â u+v)-construction based on

linear OA(256⁸, 289, F₂₅₆, 7) (dual of [289, 281, 8]-code), using
- extended algebraic-geometric code AG_e(F,281P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
  - sharp bound on the number of rational points on curves with genus 1 [i]
linear OA(256²⁹, 65538, F₂₅₆, 15) (dual of [65538, 65509, 16]-code), using
- constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
  1. linear OA(256²⁹, 65536, F₂₅₆, 15) (dual of [65536, 65507, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  2. linear OA(256²⁷, 65536, F₂₅₆, 14) (dual of [65536, 65509, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(256³⁷, 65827, F₂₅₆, 2, 15) (dual of [(65827, 2), 131617, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256³⁷, 65827, F₂₅₆, 3, 15) (dual of [(65827, 3), 197444, 16]-NRT-code)	[i]
3	Linear OOA(256³⁷, 65827, F₂₅₆, 4, 15) (dual of [(65827, 4), 263271, 16]-NRT-code)	[i]
4	Linear OOA(256³⁷, 65827, F₂₅₆, 5, 15) (dual of [(65827, 5), 329098, 16]-NRT-code)	[i]
5	Linear OOA(256³⁷, 65827, F₂₅₆, 6, 15) (dual of [(65827, 6), 394925, 16]-NRT-code)	[i]
6	Digital (22, 37, 65827)-net over F₂₅₆	[i]