Explore erasure coded rectangles

[cmwaters]

Summary

Instead of enforcing equal rows and columns, allow for rectangles which have columns twice the size of rows

Problem Definition

Imagine a set of transactions in a block that taking up 16 shares (including intershare padding). This is great because in a 4x4 square we have no tail padding. However, if the set of transactions takes up 17 shares, we need to double both axes, creating a grid of 8x8 = 64 shares. This means 47 shares are tail padding. If we allow rectangles with sides that are powers of 2. Then we can reduce tail padding. In this example, the rectangle would be 4x8 = 32. Which only means 15 shares of tail-padding.

Proposal

Allow for rectangles with sides powers of 2. We can represent this as the area in which the area can increment in multiples of 2 instead of multiples of 4.

A lot of the current code has the idea of a square baked in so this would be a difficult adjustment to make.

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[nashqueue]

What would the erasure-coded block look like? What I mean by that is that if the ODS (Orginal Data Square) is 48. Is the EDS(Erasure coded Square) 816?

Yellow would be the ODS. That's how imagine it.

The second question is, do we still have equivalency if we erasure code yellow->blue->red and yellow->green->red?

[cmwaters]

Good question. I'm not familiar with the internals/properties of reed-solomon erasure coding so I'm not sure if there's parity (and if it's necessary)

[adlerjohn]

Tail padding is a very small issue IMO since it's known simply by looking at the block header.