「Algebraic ECCs」: Lec4 Singleton + Plotkin Bounds and RS Code

2025-01-132025-01-31 Cryptography-ECCs 27 minutes read (About 4052 words)

In this series, I will be learning Algebraic Error Correcting Codes, lectured by Mary Wootters. The lecture videos are available here. Feedback and sugguestions are always welcome! ^ - ^

Topics Covered:

Singleton Bound
Plotkin Bound
Reed-Solomon Codes
Dual View of RS Codes
Generalized RS Code

「Algebraic ECCs」: Lec3 GV Bound and q-ARY Entropy

2024-12-262024-12-26 Cryptography-ECCs 26 minutes read (About 3856 words)

In this series, I will be learning Algebraic Error Correcting Codes, lectured by Mary Wootters. The lecture videos are available here. Feedback and sugguestions are always welcome! ^ - ^

Topics Covered:

The GV Bound:
Efficiency and Maximum-Likelihood Decoding
Application: McEliece Cryptosystem
Off to Asymptopia
- Family of Codes
- q-ary Entropy
- Trade-off Between Rate and Distance

Cryptography, ECC, GV Bound, q-ary Entropy

「Algebraic ECCs」: Lec2 Linear Codes and Finite Fields

2024-12-162024-12-26 Cryptography-ECCs 19 minutes read (About 2911 words)

In this series, I will be learning Algebraic Error Correcting Codes, lectured by Mary Wootters. The lecture videos are available here. Feedback and sugguestions are always welcome! ^ - ^

Topics Covered:

Linear Algebra over $\{0, 1\}$
- Generator Matrices
- Parity-Check Matrices
Linear Algebra not Working over $\{0, 1, 2, 3\}$
Finite Fields and Linear Codes

Cryptography, ECC, Linear Code

「Algebraic ECCs」: Lec1 Basics of ECCs

2024-12-112024-12-26 Cryptography-ECCs 18 minutes read (About 2698 words)

In this series, I will be learning Algebraic Error Correcting Codes, lectured by Mary Wootters. The lecture videos are available here. Feedback and sugguestions are always welcome! ^ - ^

Topics Covered:

Basic problem in coding theory
Code and codeword
Hamming distance and minimum distance
Rate
Hamming bound on trade-off of the rate and distance

Cryptography, ECC, Hamming Bound

「Cryptography-ZKP」: Lec7 Poly-commit based on ECC

2023-08-022023-08-02 Cryptography-ZKP 30 minutes read (About 4496 words)

In this series, I will learn Zero Knowledge Proofs (ZKP) on this MOOC, lectured by Dan Boneh, Shafi Goldwasser, Dawn Song, Justin Thaler and Yupeng Zhang.
Any corrections and advice are welcome. ^ - ^

Topics:

Poly-commit based on Error-correcting Codes
Argument for Vector-Matrix Product
- Proximity Test
- Consistency Test
Linear-time encodable code based on expanders
- Lossless Expander
- Recursive Encoding with constant relative distance