MinT - Information on Result #1598694

Information on Result #1598694

Linear OOA(2²³⁸, 5592412, F₂, 4, 15) (dual of [(5592412, 4), 22369410, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁸, 5592412, F₂, 3, 15) (dual of [(5592412, 3), 16776998, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁷⁰, 2796206, F₂, 3, 15) (dual of [(2796206, 3), 8388448, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁸, 5, F₂, 3, 7) (dual of [(5, 3), 7, 8]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹⁶², 2796201, F₂, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(2²³⁸, 2796206, F₂, 7, 15) (dual of [(2796206, 7), 19573204, 16]-NRT-code)	[i]		OOA Folding