MinT - Information on Result #1302440

Information on Result #1302440

Linear OA(8⁵¹, 260, F₈, 21) (dual of [260, 209, 22]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(8⁵⁰, 258, F₈, 21) (dual of [258, 208, 22]-code), using
- trace code [i] based on linear OA(64²⁵, 129, F₆₄, 21) (dual of [129, 104, 22]-code), using
  - extended algebraic-geometric code AG_e(F,107P) [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]
linear OA(8⁵⁰, 259, F₈, 20) (dual of [259, 209, 21]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 318 049696 282331 499963 882546 383698 991672 378816 [i]
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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(8⁵¹, 260, F₈, 2, 21) (dual of [(260, 2), 469, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(8⁵¹, 260, F₈, 3, 21) (dual of [(260, 3), 729, 22]-NRT-code)	[i]
3	Digital (30, 51, 260)-net over F₈	[i]