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Reed-Muller type codes over a combinatorial simplex: an algebraic description
arXiv:2606.02819v1 Announce Type: new Abstract: Given an ordered set $B$ of a finite field, a combinatorial simplex over $B$ is defined as the set of vectors such that the positions of the entries, with respect to $B$, sum up to a fixed integer. CAP codes are Reed-Muller type codes defined over a combinatorial simplex.
Betti Numbers and Higher Weight Spectra of Reed-Muller Codes $RM_q(2,2)$
arXiv:2408.02548v3 Announce Type: replace-cross Abstract: We determine all the Betti numbers of the $q$-ary second order Reed-Muller codes of length $q^2$, and also of the elongations of matroids associated to these codes. We then use it to determine the higher weight spectra of these codes. As a special case, we recover some results of Kaplan and Matei about counting certain curves over finite fields with prescribed rational intersection points.
Reed-Muller Codes for Joint Random and Stuck-At Error Correction
arXiv:2605.21727v2 Announce Type: replace Abstract: Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the encoder, but not to the decoder. A novel recursive construction of a set of masks is developed such that it can satisfy any $s$ stuck-at errors in a $2^m$ binary sequence, when $s \leq m$. We prove that the...
CEO 'stabbed' in £2.5m family home pictured for first time as woman arrested
CEO 'stabbed' in £2.5m family home pictured for first time as woman arrested A woman has been arrested on suspicion of murder after Neil Muller, 54-year-old CEO, was found dead with stab wounds in his £2.5m family home in quiet UK village A man found dead with stab wounds at his £2.5m family home in a quiet Warwickshire village has been named as Neil Muller. The 54-year-old suffered stab wounds to his chest early on Sunday morning.
Implementation and Optimization of HQC Decoding on NPU-Integrated Devices
arXiv:2606.01968v1 Announce Type: new Abstract: Hamming Quasi-Cyclic (HQC) has been selected by NIST for standardization as an additional code-based key-encapsulation mechanism, providing algorithmic diversity alongside lattice-based post-quantum cryptography. Efficient deployment of HQC on mobile and embedded platforms, however, requires careful optimization of its decoding procedure, whose Reed-Muller and Reed-Solomon components dominate the computational cost.
La Traviata review – gripping and genuinely moving staging opens Garsington’s summer season
Garsington Opera, WormsleyLouisa Muller’s richly detailed production of Verdi’s tragedy is elevated by Madison Leonard’s magnetic Violetta and Douglas Boyd’s musical direction that reinvigorates the familiar score Day breaks in Paris at the end of act one of La Traviata – and, at Garsington Opera’s theatre, half-open to the surrounding Chiltern countryside, the birds provide the dawn chorus. If that registers as a felicitous but accidental touch in Garsington’s first ever production of...
World Cup 2026 in numbers: Key statistical goals, titles and age records
World Cup 2026 in numbers: Key statistical goals, titles and age records The 2026 World Cup has already set records for the most host nations, most matches, and highest prize money. The 2026 FIFA World Cup has already set records for being the grandest tournament to date – most host nations, most matches and organisers’ claims of record attendance. For the first time in history, three nations will be hosting the global showpiece – Canada, Mexico and the United States – across 16 cities,...
World Cup Rank: The 50 best players in the 2026 to...
As silly as it might seem, whoever wins the 2026 World Cup is going to have an outsize impact on who the soccer world decides is the best soccer player in the world. Sure, there are 11 players on each team. And OK, fine, the best players have possession of the ball for only about three total minutes every match.
North Korea, China agree to boost ties as Xi makes rare visit
Leaders of North Korea and China agree to boost ties Published June 8, 2026last updated June 8, 2026Chinese President Xi Jinping and North Korean leader Kim Jong Un have agreed to deepen the ties between their countries as Xi attended a bilateral summit in Pyongyang in a likely bid to reassert Beijing's exclusive influence over its neighbor. Xi touched down in Pyongyang on Monday for a two-day visit — his first to North Korea since 2019. Leaders express their hopes for better relations...