MinT - Information on Result #2185119

Information on Result #2185119

Linear OA(2²¹⁵, 231, F₂, 98) (dual of [231, 16, 99]-code), using strength reduction based on linear OA(2²¹⁵, 231, F₂, 99) (dual of [231, 16, 100]-code), using

concatenation of two codes [i] based on
1. linear OA(4⁶⁹, 77, F₄, 49) (dual of [77, 8, 50]-code), using
  - constructionÂ X applied to C([0,25]) âŠ‚ C([0,21]) [i] based on
    1. linear OA(4⁶³, 65, F₄, 51) (dual of [65, 2, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 65Â | 4⁶âˆ’1, defining interval IÂ =Â [0,25], and minimum distance dÂ â‰¥ |{−15,−4,7,…,15}|+1Â =Â 52 (BCH-bound) [i]
    2. linear OA(4⁵⁷, 65, F₄, 43) (dual of [65, 8, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 65Â | 4⁶âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
    3. linear OA(4⁶, 12, F₄, 5) (dual of [12, 6, 6]-code), using
      - extended quadratic residue code Q_e(12,4) [i]
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(2²¹⁴, 230, F₂, 97) (dual of [230, 16, 98]-code)	[i]	Truncation
2	Linear OA(2²¹³, 229, F₂, 96) (dual of [229, 16, 97]-code)	[i]
3	Linear OA(2²¹¹, 227, F₂, 94) (dual of [227, 16, 95]-code)	[i]
4	Linear OA(2²¹⁰, 226, F₂, 93) (dual of [226, 16, 94]-code)	[i]
5	Linear OA(2²⁰⁷, 223, F₂, 90) (dual of [223, 16, 91]-code)	[i]
6	Linear OOA(2²¹⁵, 77, F₂, 3, 98) (dual of [(77, 3), 16, 99]-NRT-code)	[i]	OOA Folding