MinT - Information on Result #663142

Information on Result #663142

Linear OA(7²⁴, 32949, F₇, 5) (dual of [32949, 32925, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(7⁰, 4707, F₇, 0) (dual of [4707, 4707, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]
linear OA(7⁰, 4707, F₇, 0) (dual of [4707, 4707, 1]-code) (see above)
linear OA(7¹, 4707, F₇, 1) (dual of [4707, 4706, 2]-code), using
- discarding factors / shortening the dual code 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 OA(7¹, 4707, F₇, 1) (dual of [4707, 4706, 2]-code) (see above)
linear OA(7¹, 4707, F₇, 1) (dual of [4707, 4706, 2]-code) (see above)
linear OA(7⁶, 4707, F₇, 2) (dual of [4707, 4701, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁶, 16807, F₇, 2) (dual of [16807, 16801, 3]-code), using
  - an extension C_e(1) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [i]
linear OA(7¹⁵, 4707, F₇, 5) (dual of [4707, 4692, 6]-code), using
- 1 times code embedding in larger space [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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7²⁴, 16474, F₇, 2, 5) (dual of [(16474, 2), 32924, 6]-NRT-code)	[i]		OOA Folding