Section Definitions and Algorithms
This page contains definitions of important terms and algorithms used throughout the course.
Subsection Definitions
Definition 4 t-error correcting code
Definition 5 t-error detecting code
Definition 6 Maximum likelihood decoding
Definition 7 Nearest neighbor decoding
Definition 9 Hamming sphere
Definition 10 Span of vectors
Definition 11 Linear independence
Definition 12 Basis
Definition 13 Dimension
Definition 14 Rowspace
Definition 18 Generator Matrix
Definition 19 Parity-Check Matrix
Definition 20 Inner Product
Definition 21 Orthogonality
Definition 22 Orthogonal Complement/Dual Code
Definition 32 Maximum Distance Separable (MDS) Codes
Definition 33 Coset of a Subspace
Definition 34 Volume of a Hamming Sphere
Definition 37 Syndrome
Definition 38 Standard Array
Definition 41 Perfect Code
Definition 44 GCD of Polynomials
Definition 47 Irreducible Polynomials
Definition 48 Quotient of a Polynomial Ring
Subsection Algorithms
Algorithm 24 Efficient Decoding Algorithm for 1-error Correcting Linear Codes
Algorithm 28 Syndrome Decoding
Algorithm 39 Standard Array Decoding
Algorithm 45 Euclid’s Algorithm
Algorithm 51 Step-by-step Decoding Algorithm for Binary Linear Codes
