Talk
Optimized constructions of nested code pairs
Talk by Prof. Dr. Olav Geil
Speaker invited by: Prof. Dr. Joachim Rosenthal
Date: 21.03.18 Time: 15.00 - 16.00 Room: Y27H28
Nested code pairs C_2 ⊂ C_1 play a crucial role in the construction of both secret sharing schemes and quantum codes. Although the two applications at a first glance may seem very different, in both cases it is the relative distances of the nested codes that describe the most important parameters of the systems. By the relative distance of a code pair we mean the minimum Hamming weight of a word in C_1\C_2 (we only consider linear codes). Considering the relative distances of C_2 ⊂ C_1 and C_1^{⊥} ⊂ C_2^{⊥} one obtains information on information recovery and leakage for the secret sharing scheme. Similarly, one obtains information on the ability of the corresponding quantum code to correct phase-shift errors and bit-flip errors. In this talk we present improved constructions of nested code pairs giving us secret sharing schemes and quantum codes with desirable parameters.
The talk comprises joint works with C. Galindo, F. Hernando, D. Ruano, and with R. B. Christensen.