MinT - Information on Result #1312027

Information on Result #1312027

Linear OA(8¹⁷, 178, F₈, 7) (dual of [178, 161, 8]-code), using 15 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 14 times 0) based on linear OA(8¹⁶, 162, F₈, 7) (dual of [162, 146, 8]-code), using

trace code [i] based on linear OA(64⁸, 81, F₆₄, 7) (dual of [81, 73, 8]-code), using
- extended algebraic-geometric code AG_e(F,73P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 81, using
  - sharp bound on the number of rational points on curves with genus 1 [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(8¹⁷, 178, F₈, 2, 7) (dual of [(178, 2), 339, 8]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(8¹⁷, 178, F₈, 3, 7) (dual of [(178, 3), 517, 8]-NRT-code)	[i]
3	Digital (10, 17, 178)-net over F₈	[i]