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 41 Coset of a Subspace
Definition 42 Volume of a Hamming Sphere
Definition 45 Primitive Element
Definition 46 Extension Field/Subfield
Definition 47 Extension Degree
Definition 49 Syndrome Polynomial
Definition 50 Error Locator Polynomial
Definition 51 Error Evaluator Polynomial
Definition 52 Key Equation
Definition 54 Syndrome
Definition 55 Standard Array
Definition 58 Perfect Code
Definition 61 GCD of Polynomials
Definition 64 Irreducible Polynomials
Definition 65 Quotient of a Polynomial Ring
Definition 66 Characteristic of a Field
Definition 67 Prime Subfield
Definition 68 Zech’s Log Table
Definition 73 GRS Codes
Definition 74 RS Codes
Subsection Algorithms
Algorithm 24 Efficient Decoding Algorithm for 1-error Correcting Linear Codes
Algorithm 28 Syndrome Decoding
Algorithm 56 Standard Array Decoding
Algorithm 62 Euclid’s Algorithm
Algorithm 76 Sugiyama’s Algorithm for GRS Decoding
Algorithm 77 Extended Euclidean Algorithm
Algorithm 82 Decoding Algorithm for the Double-Error-Correcting Alternant Code over GF(2)
Algorithm 83 Step-by-step Decoding Algorithm for Binary Linear Codes
