MinT - Information on Result #1604779

Information on Result #1604779

Linear OOA(3¹⁴⁴, 3541478, F₃, 4, 14) (dual of [(3541478, 4), 14165768, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴⁴, 3541478, F₃, 2, 14) (dual of [(3541478, 2), 7082812, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁴⁴, 4194308, F₃, 2, 14) (dual of [(4194308, 2), 8388472, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁸, 7, F₃, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,6P) [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(3¹³⁶, 4194301, F₃, 2, 14) (dual of [(4194301, 2), 8388466, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹³⁶, 8388602, F₃, 14) (dual of [8388602, 8388466, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹³⁶, large, F₃, 14) (dual of [large, large−136, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(3¹⁴⁴, 1770738, F₃, 20, 14) (dual of [(1770738, 20), 35414616, 15]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row