MinT - Information on Result #1640180

Information on Result #1640180

Linear OOA(2²⁵⁶, 2098515, F₂, 5, 18) (dual of [(2098515, 5), 10492319, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵⁶, 2098515, F₂, 4, 18) (dual of [(2098515, 4), 8393804, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁹, 1365, F₂, 4, 9) (dual of [(1365, 4), 5411, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴⁹, 1365, F₂, 3, 9) (dual of [(1365, 3), 4046, 10]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2⁴⁹, 4095, F₂, 9) (dual of [4095, 4046, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁴⁹, 4096, F₂, 9) (dual of [4096, 4047, 10]-code), using
        an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
2. linear OOA(2²⁰⁷, 2097150, F₂, 4, 18) (dual of [(2097150, 4), 8388393, 19]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2²⁰⁷, 8388600, F₂, 18) (dual of [8388600, 8388393, 19]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(2²⁵⁶, 1049257, F₂, 25, 18) (dual of [(1049257, 25), 26231169, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row