Effect of risk status for severe COVID-19 on individual contact behaviour during the SARS-CoV-2 pandemic in 2020/2021-an analysis based on the German COVIMOD study.

BACKGROUND: One of the primary aims of contact restriction measures during the SARS-CoV-2 pandemic has been to protect people at increased risk of severe disease from the virus. Knowledge about the uptake of contact restriction measures in this group is critical for public health decision-making. We analysed data from the German contact survey COVIMOD to assess differences in contact patterns based on risk status, and compared this to pre-pandemic data to establish whether there was a differential response to contact reduction measures. METHODS: We quantified differences in contact patterns according to risk status by fitting a generalised linear model accounting for within-participant clustering to contact data from 31 COVIMOD survey waves (April 2020-December 2021), and estimated the population-averaged ratio of mean contacts of persons with high risk for a severe COVID-19 outcome due to age or underlying health conditions, to those without. We then compared the results to pre-pandemic data from the contact surveys HaBIDS and POLYMOD. RESULTS: Averaged across all analysed waves, COVIMOD participants reported a mean of 3.21 (95% confidence interval (95%CI) 3.14,3.28) daily contacts (truncated at 100), compared to 18.10 (95%CI 17.12,19.06) in POLYMOD and 28.27 (95%CI 26.49,30.15) in HaBIDS. After adjusting for confounders, COVIMOD participants aged 65 or above had 0.83 times (95%CI 0.79,0.87) the number of contacts as younger age groups. In POLYMOD, this ratio was 0.36 (95%CI 0.30,0.43). There was no clear difference in contact patterns due to increased risk from underlying health conditions in either HaBIDS or COVIMOD. We also found that persons in COVIMOD at high risk due to old age increased their non-household contacts less than those not at such risk after strict restriction measures were lifted. CONCLUSIONS: Over the course of the SARS-CoV-2 pandemic, there was a general reduction in contact numbers in the German population and also a differential response to contact restriction measures based on risk status for severe COVID-19. This differential response needs to be taken into account for parametrisations of mathematical models in a pandemic setting

Efficient Decoding of Interleaved Subspace and Gabidulin Codes beyond their Unique Decoding Radius Using Gröbner Bases

An interpolation-based decoding scheme for L-interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a polynomial-time probabilistic unique decoder. Both interpretations allow to decode interleaved subspace codes beyond half the minimum subspace distance. Both schemes can decode γ insertions and δ deletions up to γ + Lδ ≤ L(nt − k), where nt is the dimension of the transmitted subspace and k is the number of data symbols from the field Fqm. Further, a complementary decoding approach is presented which corrects γ insertions and δ deletions up to Lγ +δ ≤ L(nt −k). Both schemes use properties of minimal Gr¨obner bases for the interpolation module that allow predicting the worst-case list size right after the interpolation step. An efficient procedure for constructing the required minimal Gr¨obner basis using the general K¨otter interpolation is presented. A computationally- and memory-efficient root-finding algorithm for the probabilistic unique decoder is proposed. The overall complexity of the decoding algorithm is at most O(L2n2 r) operations in F qm where nr is the dimension of the received subspace and L is the interleaving order. The analysis as well as the efficient algorithms can also be applied for accelerating the decoding of interleaved Gabidulin codes

Efficient Decoding of Interleaved Subspace and Gabidulin Codes beyond their Unique Decoding Radius Using Gröbner Bases

An interpolation-based decoding scheme for L-interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a polynomial-time probabilistic unique decoder. Both interpretations allow to decode interleaved subspace codes beyond half the minimum subspace distance. Both schemes can decode γ insertions and δ deletions up to γ + Lδ ≤ L(nt − k), where nt is the dimension of the transmitted subspace and k is the number of data symbols from the field Fqm. Further, a complementary decoding approach is presented which corrects γ insertions and δ deletions up to Lγ +δ ≤ L(nt −k). Both schemes use properties of minimal Gr¨obner bases for the interpolation module that allow predicting the worst-case list size right after the interpolation step. An efficient procedure for constructing the required minimal Gr¨obner basis using the general K¨otter interpolation is presented. A computationally- and memory-efficient root-finding algorithm for the probabilistic unique decoder is proposed. The overall complexity of the decoding algorithm is at most O(L2n2 r) operations in F qm where nr is the dimension of the received subspace and L is the interleaving order. The analysis as well as the efficient algorithms can also be applied for accelerating the decoding of interleaved Gabidulin codes

Code-Based Cryptography

9th International Workshop, CBCrypto 2021 Munich, Germany, June 21–22, 2021 Revised Selected Paper

Improved decoding and error floor analysis of staircase codes

Staircase codes play an important role as error-correcting codes in optical communications. In this paper, a low-complexity method for resolving stall patterns when decoding staircase codes is described. Stall patterns are the dominating contributor to the error floor in the original decoding method. Our improvement is based on locating stall patterns by intersecting non- zero syndromes and flipping the corresponding bits. The approach effectively lowers the error floor and allows for a new range of block sizes to be considered for optical communications at a certain code rate or, alternatively, a significantly decreased error floor for the same block size. Further, an improved error floor analysis is introduced which provides a more accurate estimation of the contributions to the error floor

Rank-Metric Codes and Their Applications

The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a variety of applications. In code-based cryptography, the hardness of the corresponding generic decoding problem can lead to systems with reduced public-key size. In distributed data storage, codes in the rank metric have been used repeatedly to construct codes with locality, and in coded caching, they have been employed for the placement of coded symbols. This survey gives a general introduction to rank-metric codes, explains their most important applications, and highlights their relevance to these areas of research

Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius

International audienc