MinT - Information on Result #1440654

Information on Result #1440654

Linear OOA(7¹⁶, 4714, F₇, 2, 5) (dual of [(4714, 2), 9412, 6]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(7¹⁶, 4714, F₇, 5) (dual of [4714, 4698, 6]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(7², 8, F₇, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
  - extended Reedâ€“Solomon code RS_e(6,7) [i]
  - Hamming code H(2,7) [i]
  - algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using the rational function field F₇(x) [i]
2. linear OA(7¹⁴, 4706, F₇, 5) (dual of [4706, 4692, 6]-code), using
  - trace code [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
    - a code by Danev and Olsson [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		This result only	Method
1	Linear OOA(7¹⁶, 4713, F₇, 3, 5) (dual of [(4713, 3), 14123, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(7¹⁶, 4713, F₇, 6, 5) (dual of [(4713, 6), 28262, 6]-NRT-code)	[i]		OOA Stacking with Additional Row