MinT - Information on Result #1297154

Information on Result #1297154

Linear OA(256⁶², 65827, F₂₅₆, 25) (dual of [65827, 65765, 26]-code), using (u,Â u+v)-construction based on

linear OA(256¹³, 289, F₂₅₆, 12) (dual of [289, 276, 13]-code), using
- extended algebraic-geometric code AG_e(F,276P) [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(256⁴⁹, 65538, F₂₅₆, 25) (dual of [65538, 65489, 26]-code), using
- constructionÂ X applied to C_e(24) âŠ‚ C_e(23) [i] based on
  1. linear OA(256⁴⁹, 65536, F₂₅₆, 25) (dual of [65536, 65487, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  2. linear OA(256⁴⁷, 65536, F₂₅₆, 24) (dual of [65536, 65489, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [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(256⁶², 65827, F₂₅₆, 2, 25) (dual of [(65827, 2), 131592, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁶², 65827, F₂₅₆, 3, 25) (dual of [(65827, 3), 197419, 26]-NRT-code)	[i]
3	Linear OOA(256⁶², 65827, F₂₅₆, 4, 25) (dual of [(65827, 4), 263246, 26]-NRT-code)	[i]
4	Linear OOA(256⁶², 65827, F₂₅₆, 5, 25) (dual of [(65827, 5), 329073, 26]-NRT-code)	[i]
5	Linear OOA(256⁶², 65827, F₂₅₆, 6, 25) (dual of [(65827, 6), 394900, 26]-NRT-code)	[i]
6	Digital (37, 62, 65827)-net over F₂₅₆	[i]