MinT - Information on Result #1316328

Information on Result #1316328

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) 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		Method
1	Linear OOA(256⁶⁵, 1047, F₂₅₆, 2, 38) (dual of [(1047, 2), 2029, 39]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁶⁵, 1047, F₂₅₆, 3, 38) (dual of [(1047, 3), 3076, 39]-NRT-code)	[i]
3	Linear OOA(256⁶⁵, 1047, F₂₅₆, 4, 38) (dual of [(1047, 4), 4123, 39]-NRT-code)	[i]
4	Linear OOA(256⁶⁵, 1047, F₂₅₆, 5, 38) (dual of [(1047, 5), 5170, 39]-NRT-code)	[i]
5	Linear OOA(256⁶⁵, 1047, F₂₅₆, 6, 38) (dual of [(1047, 6), 6217, 39]-NRT-code)	[i]
6	Digital (27, 65, 1047)-net over F₂₅₆	[i]