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Related Articles from SNS
Shortest LCD embeddings of binary, ternary and quaternary linear codes
arXiv:2601.20600v2 Announce Type: replace Abstract: In the recent years, there has been active research on self-orthogonal embeddings of linear codes since they yielded some optimal self-orthogonal codes. LCD codes have a trivial hull so they are counterparts of self-orthogonal codes. So it is a natural question whether one can embed linear codes into optimal LCD codes.
Embedding linear codes over Z4 into self-orthogonal codes
Announce Type: new Abstract: The purpose of this paper is to investigate the self-orthogonal embedding problem for linear codes over Z4. We propose several tight bounds on the length of the shortest self-orthogonal embedding over Z4, and determine the exact shortest self-orthogonal embedding length under specific conditions. As an example satisfying these conditions, we establish the exact length of the shortest self-orthogonal embedding for the quaternary Preparata codes.
Britain's oldest cave art may have been rediscovered in Bacon Hole cave
June 2, 2026 report Britain's oldest cave art may have been rediscovered in Bacon Hole cave Paul Arnold Author Gaby Clark Scientific Editor Robert Egan Associate Editor The oldest cave art in Britain may have been discovered, or more likely rediscovered, in a cave on the Gower Peninsula in South Wales, possibly dating back around 17,000 years. The red stripe markings on the walls of a cave called Bacon Hole were first spotted in 1912. They were hailed by their finders, Professor William...
17,000-year-old stripes of red in a Welsh cave are the oldest rock art in the UK, study finds
17,000-year-old stripes of red in a Welsh cave are the oldest rock art in the UK, study finds Over a century after a red-lined cave wall was discovered, scientists have determined that it represents the U.K.'s oldest rock art. For a century, experts dismissed a series of parallel red lines discovered in a Welsh cave as a phenomenon of nature rather than human-made rock art. But a new study shows the lines are a rare example of Paleolithic art — and at 17,000 years old, they're the earliest...
Stonehenge Altar Stone's epic transportation across ancient Britain detailed in new study
Stonehenge Altar Stone's epic transportation across ancient Britain detailed in new study Robert Egan Associate Editor New research by Curtin University has revealed how one of Stonehenge's most mysterious stones was likely transported hundreds of kilometers across Britain through challenging terrain, highlighting the remarkable capabilities of ancient communities. Stonehenge's central Altar Stone is a six-tonne sandstone megalith now believed to have originated in northeast Scotland, around...
Stonehenge's altar stone probably wasn't transported by a glacier
Researchers investigating the origins of Stonehenge’s enigmatic altar stone say it is possible that the 6-tonne rock was carried southwards from Scotland by a glacier – but this hypothesis relies on an unlikely series of events, making it more likely that humans transported it. The 5-metre-long monolith, which is partially buried and overlain by two other stones, has been in its present location, at the centre of Stonehenge’s ring of worked boulders, for around 4500 years. In 2024,...
Stonehenge's most mysterious stone traveled 700 kilometers across Britain
Stonehenge's most mysterious stone traveled 700 kilometers across Britain - Date: - June 9, 2026 - Source: - Curtin University - Summary: - Scientists have uncovered new evidence that Stonehenge’s six-ton Altar Stone was deliberately transported hundreds of kilometers from Scotland by ancient people. The feat would have required extraordinary planning, teamwork, and determination, revealing a surprisingly sophisticated level of organization thousands of years ago. A new study led by...
What really happened when ancient humans migrated out of Africa
This is an extract from Our Human Story, our newsletter about the revolution in archaeology. Sign up to receive it in your inbox every month. The great out-of-Africa migration is one of the canonical events in the human evolutionary story.
Red stripes declared U.K.’s oldest art after being dismissed as a natural phenomenon
LONDON — Dismissed as a natural phenomenon for more than a century, red stripes on a rock in Wales have been found to be the oldest known prehistoric art in Britain and northwestern Europe — created by human fingers 17,100 years ago, according to new research. An international team of scientists revisited Bacon Hole, a cave near Mumbles in South Wales, to re-examine the series of red-pigmented horizontal stripes on a panel first discovered there in 1912. The markings were initially...
LLM-Guided Search for Deletion-Correcting Codes
arXiv:2504.00613v2 Announce Type: replace Abstract: Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. We adapt FunSearch, a large language model (LLM)-guided evolutionary search, to discover functions that construct deletion-correcting codes at short code lengths. For a single deletion, our search finds a function that we prove constructs the conjectured-optimal Varshamov-Tenengolts code.