- galois.ReedSolomon.detect(codeword: ArrayLike) bool_ | ndarray
Detects if errors are present in the Reed-Solomon codeword \(\mathbf{c}\).
The \([n, k, d]_q\) Reed-Solomon code has \(d_{min} = d\) minimum distance. It can detect up to \(d_{min}-1\) errors.
- Parameters¶
- Returns¶
A boolean scalar or array indicating if errors were detected in the corresponding codeword
True
or notFalse
.
Examples¶
Encode a single message using the \(\textrm{RS}(15, 9)\) code.
In [1]: rs = galois.ReedSolomon(15, 9) In [2]: GF = rs.field In [3]: m = GF.Random(rs.k); m Out[3]: GF([ 2, 6, 10, 2, 2, 10, 10, 12, 5], order=2^4) In [4]: c = rs.encode(m); c Out[4]: GF([ 2, 6, 10, 2, 2, 10, 10, 12, 5, 2, 12, 12, 14, 4, 8], order=2^4)
Detect no errors in the valid codeword.
In [5]: rs.detect(c) Out[5]: False
Detect \(d_{min}-1\) errors in the codeword.
In [6]: rs.d Out[6]: 7 In [7]: e = GF.Random(rs.d - 1, low=1); e Out[7]: GF([ 6, 11, 10, 7, 14, 13], order=2^4) In [8]: c[0:rs.d - 1] += e; c Out[8]: GF([ 4, 13, 0, 5, 12, 7, 10, 12, 5, 2, 12, 12, 14, 4, 8], order=2^4) In [9]: rs.detect(c) Out[9]: True
Encode a single message using the shortened \(\textrm{RS}(11, 5)\) code.
In [10]: rs = galois.ReedSolomon(15, 9) In [11]: GF = rs.field In [12]: m = GF.Random(rs.k - 4); m Out[12]: GF([11, 8, 12, 9, 5], order=2^4) In [13]: c = rs.encode(m); c Out[13]: GF([11, 8, 12, 9, 5, 13, 14, 15, 14, 12, 9], order=2^4)
Detect no errors in the valid codeword.
In [14]: rs.detect(c) Out[14]: False
Detect \(d_{min}-1\) errors in the codeword.
In [15]: rs.d Out[15]: 7 In [16]: e = GF.Random(rs.d - 1, low=1); e Out[16]: GF([10, 11, 7, 8, 8, 1], order=2^4) In [17]: c[0:rs.d - 1] += e; c Out[17]: GF([ 1, 3, 11, 1, 13, 12, 14, 15, 14, 12, 9], order=2^4) In [18]: rs.detect(c) Out[18]: True
Encode a matrix of three messages using the \(\textrm{RS}(15, 9)\) code.
In [19]: rs = galois.ReedSolomon(15, 9) In [20]: GF = rs.field In [21]: m = GF.Random((3, rs.k)); m Out[21]: GF([[10, 2, 1, 14, 14, 15, 2, 15, 15], [ 3, 7, 1, 12, 5, 4, 3, 3, 13], [12, 15, 11, 4, 11, 12, 12, 15, 9]], order=2^4) In [22]: c = rs.encode(m); c Out[22]: GF([[10, 2, 1, 14, 14, 15, 2, 15, 15, 13, 11, 11, 12, 1, 15], [ 3, 7, 1, 12, 5, 4, 3, 3, 13, 3, 5, 6, 0, 3, 4], [12, 15, 11, 4, 11, 12, 12, 15, 9, 2, 8, 5, 3, 11, 6]], order=2^4)
Detect no errors in the valid codewords.
In [23]: rs.detect(c) Out[23]: array([False, False, False])
Detect one, two, and \(d_{min}-1\) errors in the codewords.
In [24]: rs.d Out[24]: 7 In [25]: c[0,0:1] += GF.Random(1, low=1) In [26]: c[1,0:2] += GF.Random(2, low=1) In [27]: c[2, 0:rs.d - 1] += GF.Random(rs.d - 1, low=1) In [28]: c Out[28]: GF([[ 4, 2, 1, 14, 14, 15, 2, 15, 15, 13, 11, 11, 12, 1, 15], [ 9, 5, 1, 12, 5, 4, 3, 3, 13, 3, 5, 6, 0, 3, 4], [ 8, 5, 10, 2, 12, 5, 12, 15, 9, 2, 8, 5, 3, 11, 6]], order=2^4) In [29]: rs.detect(c) Out[29]: array([ True, True, True])
Encode a matrix of three messages using the shortened \(\textrm{RS}(11, 5)\) code.
In [30]: rs = galois.ReedSolomon(15, 9) In [31]: GF = rs.field In [32]: m = GF.Random((3, rs.k - 4)); m Out[32]: GF([[ 4, 6, 4, 4, 11], [ 9, 13, 15, 6, 1], [ 5, 11, 12, 6, 5]], order=2^4) In [33]: c = rs.encode(m); c Out[33]: GF([[ 4, 6, 4, 4, 11, 4, 5, 15, 2, 11, 14], [ 9, 13, 15, 6, 1, 10, 10, 10, 13, 2, 10], [ 5, 11, 12, 6, 5, 9, 8, 12, 2, 1, 13]], order=2^4)
Detect no errors in the valid codewords.
In [34]: rs.detect(c) Out[34]: array([False, False, False])
Detect one, two, and \(d_{min}-1\) errors in the codewords.
In [35]: rs.d Out[35]: 7 In [36]: c[0,0:1] += GF.Random(1, low=1) In [37]: c[1,0:2] += GF.Random(2, low=1) In [38]: c[2, 0:rs.d - 1] += GF.Random(rs.d - 1, low=1) In [39]: c Out[39]: GF([[ 7, 6, 4, 4, 11, 4, 5, 15, 2, 11, 14], [11, 3, 15, 6, 1, 10, 10, 10, 13, 2, 10], [10, 10, 15, 4, 11, 4, 8, 12, 2, 1, 13]], order=2^4) In [40]: rs.detect(c) Out[40]: array([ True, True, True])