MinT - Information on Result #1536088

Information on Result #1536088

Linear OOA(4¹¹⁶, 4194310, F₄, 3, 13) (dual of [(4194310, 3), 12582814, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹¹⁶, 4194310, F₄, 2, 13) (dual of [(4194310, 2), 8388504, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁷, 9, F₄, 2, 6) (dual of [(9, 2), 11, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,11P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
2. linear OOA(4¹⁰⁹, 4194301, F₄, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁰⁹, 8388602, F₄, 13) (dual of [8388602, 8388493, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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(4¹¹⁶, 2097154, F₄, 15, 13) (dual of [(2097154, 15), 31457194, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row