MinT - Information on Result #1640539

Information on Result #1640539

Linear OOA(2²⁶⁰, 2099811, F₂, 5, 18) (dual of [(2099811, 5), 10498795, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁶⁰, 2099811, F₂, 4, 18) (dual of [(2099811, 4), 8398984, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵³, 2661, F₂, 4, 9) (dual of [(2661, 4), 10591, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁵³, 2661, F₂, 3, 9) (dual of [(2661, 3), 7930, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2⁵³, 2731, F₂, 3, 9) (dual of [(2731, 3), 8140, 10]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(2⁵³, 8193, F₂, 9) (dual of [8193, 8140, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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(2²⁶⁰, 1049905, F₂, 25, 18) (dual of [(1049905, 25), 26247365, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row