MinT - Information on Result #736048

Information on Result #736048

Linear OA(256³², 66052, F₂₅₆, 12) (dual of [66052, 66020, 13]-code), using (u,Â u+v)-construction based on

linear OA(256⁹, 514, F₂₅₆, 6) (dual of [514, 505, 7]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(256³, 257, F₂₅₆, 3) (dual of [257, 254, 4]-code or 257-arc in PG(2,256) or 257-cap in PG(2,256)), using
    - extended Reedâ€“Solomon code RS_e(254,256) [i]
    - algebraic-geometric code AG(F, Q+125P) with degQ = 3 and 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, Q+83P) with degQ = 4 and 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+50P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  2. linear OA(256⁶, 257, F₂₅₆, 6) (dual of [257, 251, 7]-code or 257-arc in PG(5,256)), using
    - extended Reedâ€“Solomon code RS_e(251,256) [i]
    - algebraic-geometric code AG(F,125P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
    - algebraic-geometric code AG(F, Q+82P) with degQ = 4 and 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,50P) with degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
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(256³², 33026, F₂₅₆, 2, 12) (dual of [(33026, 2), 66020, 13]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256³², 22017, F₂₅₆, 3, 12) (dual of [(22017, 3), 66019, 13]-NRT-code)	[i]		OOA Folding