Add system function definitions

headers/system.h

 #ifndef SYSTEM_H
 #define SYSTEM_H
 
+#include <stdint.h>
+
 typedef struct
 {
     // TODO
 } system_t;
 
+/**
+ *
+ * Add two vectors in a Galois Field 256
+ * @param symbol_1: the first symbol to add
+ * @param symbol_2: the second symbol to add
+ * @param symbol_size: size of the two symbols (of the same size!)
+ * @return: a new vector of `symbol_size` byte containing the result of symbol_1 + symbol_2 in GF(256)
+ */
+uint8_t *gf256_add_two_vectors(uint8_t *symbol_1, uint8_t *symbol_2, uint32_t symbol_size);
+
+/**
+ *
+ * Add two vectors in a Galois Field 256 where the second vector is scaled
+ * @param symbol_1: the first symbol to add
+ * @param symbol_2: the second symbol to add (the scaled one)
+ * @param coef: the coefficient of the scaling
+ * @param symbol_size: size of the two symbols (of the same size!)
+ * @return: a new vector of `symbol_size` byte containing the result of symbol_1 + symbol_2 * coef in GF(256)
+ */
+uint8_t *gf256_add_two_vectors_scaled(uint8_t *symbol_1, uint8_t *symbol_2, uint8_t coef, uint32_t symbol_size);
+
+/**
+ *
+ * Divide a vector in a Galois Field 25§ by a coefficient
+ * @param symbol: the symbol to add
+ * @param coef: the dividing coefficient
+ * @param symbol_size: size of the two symbols (of the same size!)
+ * @return: a new vector of `symbol_size` byte containing the result of symbol_1 / coef
+ */
+uint8_t *gf256_divide_vector_scaled(uint8_t *symbol, uint8_t coef, uint32_t symbol_size);
+
+/**
+ *
+ * Resolve the linear system Ax=b in a Galois Field 256. The result is stored in the independent terms after the resolution
+ * @param A: matrix of coefficients
+ * @param b: independent terms
+ * @param symbol_size: size of the independent terms
+ * @param system_size: the size of the system (i.e., number of rows/columns)
+ */
+void gf256_gaussian_elimination(uint8_t **A, uint8_t **b, uint32_t symbol_size, uint32_t system_size);
+
+/**
+ *
+ * Generate all coefficients for a block
+ * @param seed: the seed to generate the coefficients
+ * @param nss: number of source symbols in a block
+ * @param nrs: number of repair symbols in a block
+ * @return: a nss * nrs array of coefficients
+ */
+uint8_t **gen_coef(uint32_t seed, uint32_t nss, uint32_t nrs);
+
 #endif /* SYSTEM_H */
\ No newline at end of file

main.c

@@ -142,19 +142,19 @@ int main(int argc, char *argv[])
         
         // You may modify or delete the following lines. This is just an example of how to use tinymt32
         uint32_t seed = 42; // Replace with the seed from the instance file!
-		
-		tinymt32_t prng;
-		memset(&prng, 0, sizeof(tinymt32_t));
-		// Do not modify these values!
-		prng.mat1 = 0x8f7011ee;
-		prng.mat2 = 0xfc78ff1f;
-		prng.tmat = 0x3793fdff;
-		tinymt32_init(&prng, seed);
-		
-		// You can generate coefficients by calling this function
-		// Do not forget that we use byte values, so we have to
-		// cast the uint32_t returned value to only keep the last 8 bits.
-		uint8_t coef = (uint8_t)tinymt32_generate_uint32(&prng);
+        
+        tinymt32_t prng;
+        memset(&prng, 0, sizeof(tinymt32_t));
+        // Do not modify these values!
+        prng.mat1 = 0x8f7011ee;
+        prng.mat2 = 0xfc78ff1f;
+        prng.tmat = 0x3793fdff;
+        tinymt32_init(&prng, seed);
+
+        // You can generate coefficients by calling this function
+        // Do not forget that we use byte values, so we have to
+        // cast the uint32_t returned value to only keep the last 8 bits.
+        uint8_t coef = (uint8_t)tinymt32_generate_uint32(&prng);
         if (args.verbose)
         {
             printf("Coefficient: %u\n", coef);