added encoder and syndrome decoder for short BCH codes

short_bch_code_decoder.hh

@@ -0,0 +1,56 @@
+/*
+Decoder for short BCH codes
+
+Copyright 2020 Ahmet Inan <inan@aicodix.de>
+*/
+
+#pragma once
+
+namespace CODE {
+
+template <int N, int K>
+class ShortBCHCodeDecoder
+{
+	static const int P = N - K;
+	static const int W = 1 << K;
+	static const int R = 1 << P;
+	int err[R];
+	short par[W];
+	static_assert(N < 8 * sizeof(err[0]), "codeword type not wide enough");
+	static_assert(P < 8 * sizeof(par[0]), "parity type not wide enough");
+	static int modgen(int inp, int gen)
+	{
+		for (int i = K-1; i >= 0; --i) {
+			int tmp = inp >> (i+P);
+			inp ^= (tmp & 1) * (gen << i);
+		}
+		return inp;
+	}
+public:
+	ShortBCHCodeDecoder(int generator, int T)
+	{
+		for (int i = 0; i < W; ++i)
+			par[i] = modgen(i << P, generator);
+		err[0] = 0;
+		assert(T > 0 && T <= 4);
+		for (int a = 1<<(N-1); T >= 1 && a; a >>= 1) {
+			err[modgen(a, generator)] = a;
+			for (int b = a >> 1; T >= 2 && b; b >>= 1) {
+				err[modgen(a|b, generator)] = a|b;
+				for (int c = b >> 1; T >= 3 && c; c >>= 1) {
+					err[modgen(a|b|c, generator)] = a|b|c;
+					for (int d = c >> 1; T >= 4 && d; d >>= 1) {
+						err[modgen(a|b|c|d, generator)] = a|b|c|d;
+					}
+				}
+			}
+		}
+	}
+	int operator()(int inp)
+	{
+		return inp ^ err[(par[inp>>P] ^ inp) & (R-1)];
+	}
+};
+
+}
+