MinT - Information on Result #1302492

Information on Result #1302492

Linear OA(8⁶³, 260, F₈, 27) (dual of [260, 197, 28]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(8⁶², 258, F₈, 27) (dual of [258, 196, 28]-code), using
- trace code [i] based on linear OA(64³¹, 129, F₆₄, 27) (dual of [129, 98, 28]-code), using
  - extended algebraic-geometric code AG_e(F,101P) [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(8⁶², 259, F₈, 26) (dual of [259, 197, 27]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8⁶²Â > V_b^sâˆ’1(kâˆ’1)Â = 51 545361 829634 584597 154261 007075 369352 148345 094350 565536 [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		This result only	Method
1	Linear OA(8⁶⁴, 269, F₈, 27) (dual of [269, 205, 28]-code)	[i]		VarÅ¡amovâ€“Edel Lengthening
2	Linear OA(8⁶⁵, 287, F₈, 27) (dual of [287, 222, 28]-code)	[i]		VarÅ¡amovâ€“Edel Lengthening