MinT - Information on Result #735960

Information on Result #735960

Linear OA(256⁴⁹, 65795, F₂₅₆, 20) (dual of [65795, 65746, 21]-code), using (u,Â u+v)-construction based on

linear OA(256¹⁰, 257, F₂₅₆, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using
- extended Reedâ€“Solomon code RS_e(247,256) [i]
- algebraic-geometric code AG(F,123P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
- algebraic-geometric code AG(F,82P) with degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+48P) with degQ = 6 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
linear OA(256³⁹, 65538, F₂₅₆, 20) (dual of [65538, 65499, 21]-code), using
- constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
  1. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
  2. linear OA(256³⁷, 65536, F₂₅₆, 19) (dual of [65536, 65499, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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		Method
1	OA(128⁵⁶, 65795, S₁₂₈, 20)	[i]	Discarding Parts of the Base for OAs
2	Linear OOA(256⁴⁹, 65795, F₂₅₆, 2, 20) (dual of [(65795, 2), 131541, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(256⁴⁹, 65795, F₂₅₆, 3, 20) (dual of [(65795, 3), 197336, 21]-NRT-code)	[i]
4	Linear OOA(256⁴⁹, 65795, F₂₅₆, 4, 20) (dual of [(65795, 4), 263131, 21]-NRT-code)	[i]
5	Linear OOA(256⁴⁹, 65795, F₂₅₆, 5, 20) (dual of [(65795, 5), 328926, 21]-NRT-code)	[i]
6	Linear OOA(256⁴⁹, 65795, F₂₅₆, 6, 20) (dual of [(65795, 6), 394721, 21]-NRT-code)	[i]
7	Digital (29, 49, 65795)-net over F₂₅₆	[i]
8	Linear OOA(256⁴⁹, 32897, F₂₅₆, 2, 20) (dual of [(32897, 2), 65745, 21]-NRT-code)	[i]	OOA Folding
9	Linear OOA(256⁴⁹, 13159, F₂₅₆, 5, 20) (dual of [(13159, 5), 65746, 21]-NRT-code)	[i]	OOA Folding