MinT - Information on Result #1312291

Information on Result #1312291

Linear OA(8⁶³, 288, F₈, 26) (dual of [288, 225, 27]-code), using 26 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 7 times 0, 1, 17 times 0) based on linear OA(8⁶¹, 260, F₈, 26) (dual of [260, 199, 27]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(8⁶⁰, 258, F₈, 26) (dual of [258, 198, 27]-code), using
  - trace code [i] based on linear OA(64³⁰, 129, F₆₄, 26) (dual of [129, 99, 27]-code), using
    - extended algebraic-geometric code AG_e(F,102P) [i] based on function field F/F₆₄ with g(F) = 4 and N(F) ≥ 129, using
      - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]
2. linear OA(8⁶⁰, 259, F₈, 25) (dual of [259, 199, 26]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁶⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 786175 140070 077847 813691 509886 798809 858889 083632 283616 [i]
3. linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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.

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(8⁶³, 288, F₈, 2, 26) (dual of [(288, 2), 513, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(8⁶³, 288, F₈, 3, 26) (dual of [(288, 3), 801, 27]-NRT-code)	[i]
3	Digital (37, 63, 288)-net over F₈	[i]