MinT - Information on Result #1642106

Information on Result #1642106

Linear OOA(3⁹⁷, 4194308, F₃, 5, 10) (dual of [(4194308, 5), 20971443, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁹⁷, 4194308, F₃, 2, 10) (dual of [(4194308, 2), 8388519, 11]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁶, 7, F₃, 2, 5) (dual of [(7, 2), 8, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁹¹, 4194301, F₃, 2, 10) (dual of [(4194301, 2), 8388511, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁹¹, 8388602, F₃, 10) (dual of [8388602, 8388511, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(3⁹⁷, 4194307, F₃, 15, 10) (dual of [(4194307, 15), 62914508, 11]-NRT-code)	[i]		OOA Stacking with Additional Row