MinT - Information on Result #2450560

Information on Result #2450560

Linear OOA(8¹⁴³, 78, F₈, 2, 118) (dual of [(78, 2), 13, 119]-NRT-code), using strength reduction based on linear OOA(8¹⁴³, 78, F₈, 2, 119) (dual of [(78, 2), 13, 120]-NRT-code), using

constructionÂ X applied to AG(2;F,8P) âŠ‚ AG(2;F,25P) [i] based on
1. linear OOA(8¹²⁶, 64, F₈, 2, 119) (dual of [(64, 2), 2, 120]-NRT-code), using algebraic-geometric NRT-code AG(2;F,8P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]
2. linear OOA(8¹¹⁵, 64, F₈, 2, 102) (dual of [(64, 2), 13, 103]-NRT-code), using algebraic-geometric NRT-code AG(2;F,25P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹⁷, 14, F₈, 2, 16) (dual of [(14, 2), 11, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,11P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

Mode: Constructive and 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(8¹⁴¹, 77, F₈, 2, 116) (dual of [(77, 2), 13, 117]-NRT-code)	[i]		Truncation for OOAs