MinT - Information on Result #2688055

Information on Result #2688055

Linear OOA(4²⁵⁹, 2796442, F₄, 3, 25) (dual of [(2796442, 3), 8389067, 26]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²⁵⁶, 2796441, F₄, 3, 25) (dual of [(2796441, 3), 8389067, 26]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4³⁹, 240, F₄, 3, 12) (dual of [(240, 3), 681, 13]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 39, 240)-net over F₄, using
    - trace code for nets [i] based on digital (1, 13, 80)-net over F₆₄, using
      - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
2. linear OOA(4²¹⁷, 2796201, F₄, 3, 25) (dual of [(2796201, 3), 8388386, 26]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(4²¹⁷, large, F₄, 25) (dual of [large, large−217, 26]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Mode: Constructive and 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(4²⁶⁰, 2796442, F₄, 3, 25) (dual of [(2796442, 3), 8389066, 26]-NRT-code)	[i]		OOA Duplication