MinT - Information on Result #906542

Information on Result #906542

Linear OOA(7²⁴, 16527, F₇, 2, 5) (dual of [(16527, 2), 33030, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁰, 2361, F₇, 2, 0) (dual of [(2361, 2), 4722, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁰, s, F₇, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(7⁰, 2361, F₇, 2, 0) (dual of [(2361, 2), 4722, 1]-NRT-code) (see above)
linear OOA(7¹, 2361, F₇, 2, 1) (dual of [(2361, 2), 4721, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹, s, F₇, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(7¹, 2361, F₇, 2, 1) (dual of [(2361, 2), 4721, 2]-NRT-code) (see above)
linear OOA(7¹, 2361, F₇, 2, 1) (dual of [(2361, 2), 4721, 2]-NRT-code) (see above)
linear OOA(7⁵, 2361, F₇, 2, 2) (dual of [(2361, 2), 4717, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁵, 2801, F₇, 2, 2) (dual of [(2801, 2), 5597, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(7⁵, 2801, F₇, 2) (dual of [2801, 2796, 3]-code), using
    - Hamming code H(5,7) [i]
linear OOA(7¹⁶, 2361, F₇, 2, 5) (dual of [(2361, 2), 4706, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7², 8, F₇, 2, 2) (dual of [(8, 2), 14, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;14,7) [i]
  2. linear OOA(7¹⁴, 2353, F₇, 2, 5) (dual of [(2353, 2), 4692, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(7¹⁴, 4706, F₇, 5) (dual of [4706, 4692, 6]-code), using
      - trace code [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
        a code by Danev and Olsson [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7²⁴, 16526, F₇, 3, 5) (dual of [(16526, 3), 49554, 6]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(7²⁴, 16526, F₇, 6, 5) (dual of [(16526, 6), 99132, 6]-NRT-code)	[i]		OOA Stacking with Additional Row