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Formal Foundations and Proof-Carrying Certificates for q-ary Covering Codes in Lean 4
Announce Type: new Abstract: Covering codes in finite Hamming spaces ask for small sets of words whose Hamming balls cover the whole space. This paper presents a Lean 4 formalization of the elementary theory of q-ary covering codes, centered on certificate predicates for upper bounds, lower bounds, and exact covering numbers $K_q(n,r)$. The formalization proves the q-ary Hamming-ball volume formula, the sphere-covering lower bound, elementary exact cases, product and relation rules, and...
C++: The Programming Language back cover raises questions not answered by front
A little while ago, we considered how the cover of the book C++: The Programming Language raises questions not answered by the cover, since the cover illustration for a book putatively about the C++ programming language shows code written in JavaScript.¹ But there’s also a question raised by the back cover. According to the blurb for the book, The topics included in it are of utmost significance and are bound to provide incredible insights to students.
Protect garden egg chairs with £16 waterproof cover that ‘stood strong’ against 40mph wind
Protect garden egg chairs with £16 waterproof cover that ‘stood strong’ against 40mph wind Keep new garden furniture dry from downpours with clever £16 cover that’s specially designed for an egg chair’s awkward shape, with shoppers saying it ‘stood strong’ in storms With rain settling in for the foreseeable future, you’ll need to keep your new garden furniture dry and protected until you can use it again. But whilst it's easy enough to cover up a sofa set or dining table, trying to securely...
Lacy, Toney, Moore lead EA Sports CFB 27 cover
Ole Miss running back Kewan Lacy, Miami wide receiver Malachi Toney and Oregon quarterback Dante Moore will lead the cast of athletes featured on the cover of EA Sports College Football 27, the video game developer announced Tuesday. Lacy, Toney and Moore are featured on the cover of the game's standard edition that releases July 9. They're joined by Indiana coach Curt Cignetti, USC quarterback Jayden Maiava, Texas pass rusher Colin Simmons and Notre Dame cornerback Leonard Moore on the...
'It was very very good': Ötzi the Iceman's body is covered in ancient yeast — and scientists just used it to make a sourdough
'It was very very good': Ötzi the Iceman's body is covered in ancient yeast — and scientists just used it to make a sourdough A new study cultivated four strains of cold-adapted yeasts that had colonized Ötzi's body shortly after his death 5,300 years ago in the Alps. Ötzi the Iceman's skin and stomach are teeming with yeasts that infiltrated his remains shortly after his murder 5,300 years ago — and some may still be active, a new study reveals. The yeast strains covering his body are...
🏈 Caleb Williams' 'Madden' cover inspired by MJ
CHICAGO -- Caleb Williams wanted to pay homage to one of the greatest athletes of all time when the Bears quarterback was selected for the cover of "Madden NFL 27." While EA Sports wanted one of two covers to feature Williams' jump pass, which is most remembered from his fourth-down throw in the Bears' come-from-behind win over the Packers in the 2025 wild-card round, Williams wanted to add the Chicago skyline behind him as a tribute to Michael Jordan. The original 1985 Air Jordan campaign...
Henry Nowak killer's dad covers face as he appears in court with Vickrum Bigwa's brother for weapons offences
Henry Nowak killer's dad covers face as he appears in court with Vickrum Bigwa's brother for weapons offences Moga Singh, 52, and Gurpreet Digwa, 27, who are on bail, appeared alongside murderer Vickrum Digwa to face six counts of possessing an offensive weapon in a private place Henry Nowak's killer's father covered his face with a notepad as he arrived at court charged with weapons offences. Moga Singh, 52 appeared alongside sons Gurpreet Digwa, 27 and murderer Vickrum Digwa, 23, to face...
‘Mud Buddha’: China official covered in sludge during mudslide while helping villagers evacuate
Advertisement ‘Mud Buddha’: China official covered in sludge during mudslide while helping villagers evacuate Tragedy averted by selfless cadre who was swept up in floodwater as he went door-to-door telling people to get to a safe place before landslide 2-MIN READ2-MIN Alice Yanin Shanghai A valiant official in China has been dubbed “Mud Buddha” after a photograph emerged of him covered in sludge while he was averting disaster by evacuating residents before a catastrophic landslide. From the...
Teacher 'pulled a sickie' to go on mate's Portugal stag do before ripping up passport to cover tracks
Teacher 'pulled a sickie' to go on mate's Portugal stag do before ripping up passport to cover tracks Joe Wilson, a Year 6 teacher at Listerdale Junior Academy in Rotherham, South Yorkshire, was on a stag-do in Lisbon when he claimed he was too sick to work, a tribunal heard A primary school teacher "pulled a sickie" so he could go join his mates on a Portugal stag do and tried to cover his tracks by ripping pages from his passport, a tribunal has found. Joe Wilson told his boss at...
Caleb Williams lands Madden NFL 27 cover, but infamous curse looms over pivotal third season
Caleb Williams will grace the cover of this year's edition of the Madden NFL video game. "Madden NFL 27" will have a photo of what's become the signature play for the Chicago Bears quarterback: a wild jump throw. The photo of Williams mimics his remarkable fourth-and-8 pass to Rome Odunze against the Green Bay Packers in the NFC Wild Card round that helped the Bears secure the victory.