Distance-Regular Graphs

Introduction A fundamental objective of cryptography is to enable two persons to communicate over an insecure channel (a public channel such as the internet) in such a way that any other person is unable to recover their message (called the plaintext ) from what is sent in its place over the channel (the ciphertext ). The transformation of the plaintext into the ciphertext is called encryption , or enciphering. Encryption-decryption is the most ancient cryptographic activity (ciphers already existed four centuries b.c.), but its nature has deeply changed with the invention of computers, because the cryptanalysis (the activity of the third person, the eavesdropper, who aims at recovering the message) can use their power. The encryption algorithm takes as input the plaintext and an encryption key K E , and it outputs the ciphertext. If the encryption key is secret, then we speak of conventional cryptography , of private key cryptography , or of symmetric cryptography . In practice, the principle of conventional cryptography relies on the sharing of a private key between the sender of a message (often called Alice in cryptography) and its receiver (often called Bob). If, on the contrary, the encryption key is public, then we speak of public key cryptography . Public key cryptography appeared in the literature in the late 1970s.

/pdf/boolean-models-and-methods-in-mathematics-computer-science-3vbrnbyptk.pdf

Boolean Models and Methods in Mathematics, Computer Science, and Engineering: Boolean Functions for Cryptography and Error-Correcting Codes

Permutation groups

A sequence of new knot invariants is constructed by using the relationship between the theory of distributive groupoids and knot theory.Bibliography: 3 titles.

http://iopscience.iop.org/article/10.1070/SM1984v047n01ABEH002630/pdf

Distributive groupoids in knot theory

A table of binary constant weight codes of length nl28 is presented. Explicit constructions are given for most of the 600 codes in the table; the majority of these codes are new. The known techniques for constructing constant weight codes are surveyed, and a table of (unrestricted) binary codes of length nl28 is given

/pdf/a-new-table-of-constant-weight-codes-7mqteex0ei.pdf

A new table of constant weight codes

Affine and projective planes

Information sets and partial permutation decoding for codes from finite geometries

By finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T(n) for any n ≥ 5.

/pdf/permutation-decoding-for-the-binary-codes-from-triangular-3qjsqmd52v.pdf

Permutation decoding for the binary codes from triangular graphs

Designs and their codes: Bibliography

We determine to what extent permutation decoding can be used for the codes from desarguesian projective and affine planes. We define the notion of s-PD-sets to correct s errors, and construct some specific small sets for s = 2 and 3 for desarguesian planes of prime order.

Jennifer D. Key

Papers

Affine and projective planes

Information sets and partial permutation decoding for codes from finite geometries

Permutation decoding for the binary codes from triangular graphs

Designs and their codes: Bibliography

Partial permutation decoding for codes from finite planes