MinT - Information on Result #1567717

Information on Result #1567717

Linear OOA(256⁶⁵, 1047, F₂₅₆, 3, 38) (dual of [(1047, 3), 3076, 39]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(256⁶⁵, 1047, F₂₅₆, 38) (dual of [1047, 982, 39]-code), using

18 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 17 times 0) [i] based on linear OA(256⁶³, 1027, F₂₅₆, 38) (dual of [1027, 964, 39]-code), using
- constructionÂ X applied to AG(F,985P) âŠ‚ AG(F,987P) [i] based on
  1. linear OA(256⁶², 1024, F₂₅₆, 38) (dual of [1024, 962, 39]-code), using algebraic-geometric code AG(F,985P) [i] based on function field F/F₂₅₆ with g(F) = 24 and N(F) ≥ 1025, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]
  2. linear OA(256⁶⁰, 1024, F₂₅₆, 36) (dual of [1024, 964, 37]-code), using algebraic-geometric code AG(F,987P) [i] based on function field F/F₂₅₆ with g(F) = 24 and N(F) ≥ 1025 (see above)
  3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

Mode: 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(256⁶⁵, 523, F₂₅₆, 5, 38) (dual of [(523, 5), 2550, 39]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256⁶⁵, 523, F₂₅₆, 6, 38) (dual of [(523, 6), 3073, 39]-NRT-code)	[i]		OOA Folding