Section Results
This page contains theorems and propositions used throughout the course.
Subsection Results
Proposition 8 Relation Between Minimum Distance and Error-Correcting Capability
Claim 25 Closest Codeword in Standard Array
Claim 26 Standard Array Unique Decoding Condition
Theorem 30 Classification of Perfect Codes
Theorem 31 Singleton Bound
Theorem 33 Fraction of [n,k,d]_q Codes
Proposition 34 Properties of Irreducibles
Claim 35 Polynomials Mod an Irreducible Form a Field
Proposition 36 Degree Mantra
Theorem 39 Finite Fields have a Primitive Element
Theorem 40 Fields of Order \(p^n\) Exist
Theorem 43 Hamming or Sphere-Packing Bound
Theorem 44 Gilbert-Varshamov Bound for General Codes
Theorem 53 Gilbert-Varshamov Bound for Linear Codes
Theorem 54 Polynomial Division & Congruence
Theorem 57 Bezout’s Identity
